**Research Area/ Research Interest: Nonlinear partial differential equations Math**

**Research Paper Topics ideas for** Masters and Ph.D. Thesis and publication

- Numerical solution and bifurcation analysis of nonlinear partial differential equations with extreme learning machines
- A computational procedure for exact solutions of Burgers’ hierarchy of nonlinear partial differential equations
- Reduced operator inference for nonlinear partial differential equations
- Three ways to solve partial differential equations with neural networks—A review
- Local extreme learning machines and domain decomposition for solving linear and nonlinear partial differential equations
- New numerical approach for time-fractional partial differential equations arising in physical system involving natural decomposition method
- Explicit tight frames for simulating a new system of fractional nonlinear partial differential equation model of Alzheimer disease
- Application of the Advanced exp (-φ (ξ))-expansion method to the Nonlinear Conformable Time-Fractional Partial Differential Equations
- A reliable algorithm to compute the approximate solution of KdV-type partial differential equations of order seven
- The optimal homotopy analysis method applied on nonlinear time-fractional hyperbolic partial differential equation s
- Analytical analysis of fractional-order multi-dimensional dispersive partial differential equations
- Solution of partial differential equations by new double integral transform (Laplace-Sumudu transform)
- An improved data-free surrogate model for solving partial differential equations using deep neural networks
- The neural network collocation method for solving partial differential equations
- Review of the methods of transition from partial to ordinary differential equations: from macro-to nano-structural dynamics
- New approximate-analytical solutions to partial differential equations via auxiliary function method
- Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)
- Use of quantum differential equations in sonic processes
- Soliton solutions of nonlinear fractional differential equations with their applications in mathematical physics
- A scientific machine learning approach to learning reduced models for nonlinear partial differential equations
- … Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition based Deep Learning Framework for Nonlinear Partial Differential Equations.
- Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
- Optical solitons of NLS-type differential equations by extended direct algebraic method
- Numerical solutions of the partial differential equations for investigating the significance of partial slip due to lateral velocity and viscous dissipation: the case of blood …
- Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasets
- The optical soliton solutions of generalized coupled nonlinear Schrödinger-Korteweg-de Vries equations
- Simple equations method (SEsM) and its connection with the inverse scattering transform method
- Optimal system, invariance analysis of fourth-Order nonlinear ablowitz-Kaup-Newell-Segur water wave dynamical equation using lie symmetry approach
- The homotopy perturbation method for fractional differential equations: part 1 Mohand transform
- Exact solutions of conformable fractional differential equations
- Inverse Problem for a Partial Differential Equation with Gerasimov–Caputo-Type Operator and Degeneration
- APIK: Active physics-informed kriging model with partial differential equations
- Painlevé analysis and traveling wave solutions of the fourth-order differential equation for pulse with non-local nonlinearity
- Analytical solutions of linear fractional partial differential equations using fractional Fourier transform
- On the complex mixed dark-bright wave distributions to some conformable nonlinear integrable models
- Methods for constructing complex solutions of nonlinear PDEs using simpler solutions
- Peridynamics enabled learning partial differential equations
- Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning
- Simple equations method (SEsM) and its particular cases: Hirota method
- Construction of different types of traveling wave solutions of the relativistic wave equation associated with the Schrödinger equation
- Partial differential equations discovery with EPDE framework: application for real and synthetic data
- A modified exp-function method for fractional partial differential equations
- New extended direct algebraic method for the resonant nonlinear Schrödinger equation with Kerr law nonlinearity
- Haar wavelet method for solving coupled system of fractional order partial differential equations
- A study of the generalized nonlinear advection-diffusion equation arising in engineering sciences
- … of the exp-function and generalized Kudryashov methods for obtaining new exact solutions of certain nonlinear conformable time partial integro-differential equations
- An analytical technique, based on natural transform to solve fractional-order parabolic equations
- An efficient numerical scheme based on Lucas polynomials for the study of multidimensional Burgers-type equations
- Explicit solutions to nonlinear Chen–Lee–Liu equation
- Variational Principles for Two Compound Nonlinear Equations with Variable Coefficients
- Generalized invariant manifolds for integrable equations and their applications
- Distinct solutions of nonlinear space–time fractional evolution equations appearing in mathematical physics via a new technique
- Soliton solutions, Painleve analysis and conservation laws for a nonlinear evolution equation
- The solution of Poisson partial differential equations via double Laplace transform method
- He–Laplace variational iteration method for solving the nonlinear equations arising in chemical kinetics and population dynamics
- Deep learning-based method coupled with small sample learning for solving partial differential equations
- Dynamics of exact soliton solutions to the coupled nonlinear system using reliable analytical mathematical approaches
- New iterative approach for the solutions of fractional order inhomogeneous partial differential equations
- Numerical solutions of coupled nonlinear fractional KdV equations using He’s fractional calculus
- Solutions of fractional order pseudo-hyperbolic telegraph partial differential equations using finite difference method
- Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities
- Homogeneous balance method and auxiliary equation method as particular cases of simple equations method (SEsM)
- The reducing rank method to solve third-order Duffing equation with the homotopy perturbation
- … framework for the numerical analysis of high-order finite difference solvers for nonlinear multi-term time-space fractional partial differential equations with time delay
- On approximate solutions for fractional system of differential equations with Caputo-Fabrizio fractional operator
- Analysis of the fractional-order local poisson equation in fractal porous media
- White noise driven stochastic partial differential equations: triviality and non-triviality
- Multiwavelet-based operator learning for differential equations
- Exact and explicit traveling wave solutions to the generalized Gardner and BBMB equations with dual high-order nonlinear terms
- On semi analytical and numerical simulations for a mathematical biological model; the time-fractional nonlinear Kolmogorov–Petrovskii–Piskunov (KPP) equation
- Some exact explicit solutions and conservation laws of Chaffee-Infante equation by Lie symmetry analysis
- Soliton wave solutions of nonlinear mathematical models in elastic rods and bistable surfaces
- Traveling wave solutions for space-time fractional Cahn Hilliard equation and space-time fractional symmetric regularized long-wave equation
- Learning thermodynamically stable and Galilean invariant partial differential equations for non-equilibrium flows
- New solitonic and rogue wave solutions of a Klein–Gordon equation with quadratic nonlinearity
- Properties of some higher-dimensional nonlinear Schrödinger equations
- Learning nonlinear dynamics with behavior ordinary/partial/system of the differential equations: looking through the lens of orthogonal neural networks
- Analytical solution of nonlinear differential equations two oscillators mechanism using Akbari–Ganji method
- The analytical solutions of Zoomeron equation via extended rational sin-cos and sinh-cosh methods
- Linearized stable spectral method to analyze two-dimensional nonlinear evolutionary and reaction-diffusion models
- Shifted fifth-kind Chebyshev Galerkin treatment for linear hyperbolic first-order partial differential equations
- Solitary wave patterns and conservation laws of fourth-order nonlinear symmetric regularized long-wave equation arising in plasma
- Approximate Numerical solutions for the nonlinear dispersive shallow water waves as the Fornberg–Whitham model equations
- Computation of traveling wave solution for nonlinear variable-order fractional model of modified equal width equation
- Searching closed form analytic solutions to some nonlinear fractional wave equations
- A deep learning approach to reduced order modelling of parameter dependent partial differential equations
- Five semi analytical and numerical simulations for the fractional nonlinear space-time telegraph equation
- Lump solutions of a nonlinear PDE containing a third-order derivative of time
- Learning elliptic partial differential equations with randomized linear algebra
- Heuristic computational design of Morlet wavelet for solving the higher order singular nonlinear differential equations
- New structures for closed-form wave solutions for the dynamical equations model related to the ion sound and Langmuir waves
- Optical soliton solutions of the generalized non-autonomous nonlinear Schrödinger equations by the new Kudryashov’s method
- The analytical solution of fractional-order Whitham–Broer–Kaup equations by an Elzaki decomposition method
- A combined meshfree exponential Rosenbrock integrator for the third-order dispersive partial differential equations
- A novel collocation approach to solve a nonlinear stochastic differential equation of fractional order involving a constant delay
- Numerical continuation and bifurcation in Nonlinear PDEs
- New soliton wave structures of nonlinear (4+ 1)-dimensional Fokas dynamical model by using different methods
- Construction of multi-wave complexiton solutions of the Kadomtsev-Petviashvili equation via two efficient analyzing techniques
- Nonlinear mathematical model and numerical algorithm for monitoring and predicting the concentration of harmful substances in the atmosphere
- Non-intrusive surrogate modeling for parametrized time-dependent partial differential equations using convolutional autoencoders
- Three semi-implicit compact finite difference schemes for the nonlinear partial integro-differential equation arising from viscoelasticity
- Exact traveling wave solutions for two prolific conformable M-Fractional differential equations via three diverse approaches
- Adomian decomposition and fractional power series solution of a class of nonlinear fractional differential equations
- ARA-residual power series method for solving partial fractional differential equations
- Traveling wave solutions to the nonlinear evolution equation using expansion method and addendum to Kudryashov’s method
- New analytical solutions for the oskolkov-type equations in fluid dynamics via a modified methodology
- Solving nonlinear PDEs using the higher order Haar wavelet method on nonuniform and adaptive grids
- A variational inequality based stochastic approximation for inverse problems in stochastic partial differential equations
- Extension of operational matrix technique for the solution of nonlinear system of Caputo fractional differential equations subjected to integral type boundary constrains
- Matrix computational collocation approach based on rational Chebyshev functions for nonlinear differential equations
- Abundant optical solitons to the Sasa-Satsuma higher-order nonlinear Schrödinger equation
- A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions
- A new (3+ 1)-dimensional Painlevé-integrable Sakovich equation: multiple soliton solutions
- Maximum principle for space and time-space fractional partial differential equations
- Mathematical control theory for stochastic partial differential equations
- On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations
- Actor-critic method for high dimensional static Hamilton–Jacobi–Bellman partial differential equations based on neural networks
- Application of combination schemes based on radial basis functions and finite difference to solve stochastic coupled nonlinear time fractional sine-Gordon equations
- He’s frequency formulation for fractal nonlinear oscillator arising in a microgravity space
- Takagi–Sugeno fuzzy-model-based event-triggered point control for semilinear partial differential equation systems using collocated pointwise measurements
- Partial differential equations
- Some applications of Wright functions in fractional differential equations
- Search for adequate closed form wave solutions to space–time fractional nonlinear equations
- The blow-up and global existence of solution to Caputo–Hadamard fractional partial differential equation with fractional Laplacian
- Exact solutions of the fractional Sharma-Tasso-Olver equation and the fractional Bogoyavlenskii’s breaking soliton equations
- Analytical study of fractional nonlinear Schrödinger equation with harmonic oscillator
- Existence and uniqueness of solutions for fractional nonlinear hybrid impulsive system
- Bilinear residual network method for solving the exactly explicit solutions of nonlinear evolution equations
- Space–time generalized finite difference nonlinear model for solving unsteady Burgers’ equations
- A computational algorithm for the numerical solution of fractional order delay differential equations
- Distributed learning machines for solving forward and inverse problems in partial differential equations
- The homogeneous balance method and its applications for finding the exact solutions for nonlinear equations
- Fundamental solutions to the stochastic perturbed nonlinear Schrödinger’s equation via gamma distribution
- New exact traveling wave solutions to the (2+ 1)-dimensional Chiral nonlinear Schrödinger equation
- An efficient numerical approach for fractional multidimensional diffusion equations with exponential memory
- Non-Newtonian based micropolar fluid flow over nonlinear starching cylinder under Soret and Dufour numbers effects
- Generalized-expansion method for some soliton wave solutions of Burgers-like and potential KdV equations
- Analytical study of soliton solutions for an improved perturbed Schrödinger equation with Kerr law non-linearity in non-linear optics by an expansion algorithm
- Lump, soliton, and interaction solutions to a generalized two-mode higher-order nonlinear evolution equation in plasma physics
- A new perspective on the study of the fractal coupled Boussinesq–Burger equation in shallow water
- Numerical solution of nonlinear delay differential equations of fractional variable-order using a novel shifted Jacobi operational matrix
- Averaging principle for impulsive stochastic partial differential equations
- An effective computational approach and sensitivity analysis to pseudo-parabolic-type equations
- Nonlinear pantograph-type diffusion PDEs: Exact solutions and the principle of analogy
- Meta-mgnet: Meta multigrid networks for solving parameterized partial differential equations
- ReLie: a Reduce program for Lie group analysis of differential equations
- Analytical and semi-analytical solutions for time-fractional Cahn–Allen equation
- Heat and mass transfer analysis for bioconvective flow of Eyring Powell nanofluid over a Riga surface with nonlinear thermal features
- Abundant exact solutions to a generalized nonlinear Schrödinger equation with local fractional derivative
- Numerical computations for Buongiorno nano fluid model on the boundary layer flow of viscoelastic fluid towards a nonlinear stretching sheet
- On successive linearization method for differential equations with nonlinear conditions
- Computational Analysis of MHD Nonlinear Radiation Casson Hybrid Nanofluid Flow at Vertical Stretching Sheet
- Extreme theory of functional connections: A fast physics-informed neural network method for solving ordinary and partial differential equations
- Solitary and periodic wave solutions to the family of new 3D fractional WBBM equations in mathematical physics
- Development of mathematical modeling of multi-phase flow of Casson rheological fluid: Theoretical approach
- A nonlinear solver based on an adaptive neural network, introduction and application to porous media flow
- On the soliton solutions for an intrinsic fractional discrete nonlinear electrical transmission line
- Periodic and solitary wave solutions to a family of new 3D fractional WBBM equations using the two-variable method
- Nonlinear vibration of fractional Kelvin–Voigt viscoelastic beam on nonlinear elastic foundation
- Explicit wave phenomena to the couple type fractional order nonlinear evolution equations
- Theory of functional connections applied to linear odes subject to integral constraints and linear ordinary integro-differential equations
- On the conformable nonlinear Schrödinger equation with second order spatiotemporal and group velocity dispersion coefficients
- A finite-difference procedure to solve weakly singular integro partial differential equation with space-time fractional derivatives
- Selectnet: Self-paced learning for high-dimensional partial differential equations
- Abundant exact solutions to the strain wave equation in micro-structured solids
- A method for constructing exact solutions of nonlinear delay PDEs
- Neural ordinary differential equations for data-driven reduced order modeling of environmental hydrodynamics
- A new numerical scheme for solving pantograph type nonlinear fractional integro-differential equations
- Abundant wave solutions to two novel KP-like equations using an effective integration method
- Physical properties for bidirectional wave solutions to a generalized fifth-order equation with third-order time-dispersion term
- Nonlinear acoustic wave structures to the Zabolotskaya-Khokholov dynamical model
- On the exact solutions to some system of complex nonlinear models
- Solitary wave solutions for the KdV-type equations in plasma: a new approach with the Kudryashov function
- Robust data-driven discovery of partial differential equations under uncertainties
- Efficient quantum algorithm for dissipative nonlinear differential equations
- An analytical Technique for Solving New Computational Solutions of the Modified Zakharov-Kuznetsov Equation Arising in Electrical Engineering
- Onset of the broad-ranging general stable soliton solutions of nonlinear equations in physics and gas dynamics
- A priori generalization analysis of the deep ritz method for solving high dimensional elliptic partial differential equations
- Conserved quantities and travelling wave profiles to the nonlinear transmission line via Lie group analysis
- Solution of third order linear and nonlinear boundary value problems of integro-differential equations using Haar wavelet method
- Explicit high-order energy-preserving methods for general Hamiltonian partial differential equations
- New traveling solutions of the fractional nonlinear KdV and ZKBBM equations with fractional operator
- Qualitative analysis and wave propagation of the nonlinear model for low-pass electrical transmission lines
- Exact solution of the time fractional variant Boussinesq-Burgers equations
- The analysis of fractional-order nonlinear systems of third order KdV and Burgers equations via a novel transform
- Computability of differential equations
- Existence and uniqueness results for two-term nonlinear fractional differential equations via a fixed point technique
- Neural partial differential equations for chaotic systems
- Numerical simulation for coupled nonlinear Schrödinger–Korteweg–de Vries and Maccari systems of equations
- Mathematical modeling and study of MHD flow of Williamson nanofluid over a nonlinear stretching plate with activation energy
- Models base study of inclined MHD of hybrid nanofluid flow over nonlinear stretching cylinder
- MIM: A deep mixed residual method for solving high-order partial differential equations
- On solution of a class of nonlinear variable order fractional reaction–diffusion equation with Mittag–Leffler kernel
- Adomian decomposition and homotopy perturbation method for the solution of time fractional partial integro-differential equations
- Numerical solution of two-dimensional stochastic time-fractional Sine–Gordon equation on non-rectangular domains using finite difference and meshfree methods
- Analysis of the fractional-order Kaup–Kupershmidt equation via novel transforms
- Physics-informed neural operator for learning partial differential equations
- Nonlocal PT-symmetric integrable equations and related Riemann–Hilbert problems
- Exponential convergence of deep operator networks for elliptic partial differential equations
- Pde-gcn: Novel architectures for graph neural networks motivated by partial differential equations
- A new semi-analytical method for solving a class of time fractional partial differential equations with variable coefficients
- On entire solutions to eikonal-type equations
- Spectral methods to solve nonlinear problems: A review
- Supplementary variable method for thermodynamically consistent partial differential equations
- Asymptotic stability of fractional order (1, 2] stochastic delay differential equations in Banach spaces
- Implicit solitary waves for one of the generalized nonlinear Schrödinger equations
- On the new exact traveling wave solutions of the time-space fractional strain wave equation in microstructured solids via the variational method
- The analytical analysis of nonlinear fractional-order dynamical models
- Research on high precision solution of fractional partial differential equations under heat conduction model
- A review on arbitrarily regular conforming virtual element methods for elliptic partial differential equations
- A solitary wave solution to the generalized Burgers-Fisher’s equation using an improved differential transform method: A hybrid scheme approach
- On the analysis of an analytical approach for fractional Caudrey-Dodd-Gibbon equations
- Nonlinear dispersion in parabolic law medium and its optical solitons
- Similarity solution of the partial differential equations that model water/magnetite nanofluid flow and heat transfer on a stretchable rotating disk subject to thermal …
- The unified technique for the nonlinear time-fractional model with the beta-derivative
- On the behaviors of solutions of systems of non-linear differential equations with multiple constant delays
- Mathematical modeling of tsunami wave propagation at mid ocean and its amplification and run-up on shore
- Abundant new exact solutions to the fractional nonlinear evolution equation via Riemann-Liouville derivative
- Numerical solutions for solving model time-fractional Fokker–Planck equation
- A new analysis of fractional-order equal-width equations via novel techniques
- Some Results on a Two Variables Pell Polynomials
- An Itô Formula for rough partial differential equations and some applications
- Dynamic selective edge-based integer/fractional-order partial differential equation for degraded document image binarization
- A radial basis function finite difference (RBF-FD) method for numerical simulation of interaction of high and low frequency waves: Zakharov–Rubenchik equations
- Abundant closed-form wave solutions and dynamical structures of soliton solutions to the (3+ 1)-dimensional BLMP equation in mathematical physics
- Tangent nonlinear equation in context of fractal fractional operators with nonsingular kernel
- Exact analytical wave solutions for space-time variable-order fractional modified equal width equation
- Numerical solution using radial basis functions for multidimensional fractional partial differential equations of type Black–Scholes
- New soliton configurations for two different models related to the nonlinear Schrödinger equation through a graded-index waveguide
- Numerical investigation of fractional-order Swift–Hohenberg equations via a Novel transform
- Data-driven modeling of nonlinear traveling waves<? A3B2 show [editpick]?>
- Numerical analysis of time-fractional Whitham-Broer-Kaup equations with exponential-decay kernel
- Dynamics of soliton solutions in saturated ferromagnetic materials by a novel mathematical method
- Design of backpropagated intelligent networks for nonlinear second-order Lane–Emden pantograph delay differential systems
- A new analytical solution of Klein–Gordon equation with local fractional derivative
- An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense
- A novel approach to find exact solutions of fractional evolution equations with non-singular kernel derivative
- A novel design of Gudermannian function as a neural network for the singular nonlinear delayed, prediction and pantograph differential models
- Neural networks-based backward scheme for fully nonlinear PDEs
- Nonlinearity-managed lump waves in a spatial symmetric HSI model
- A pseudo-spectral fourier collocation method for inhomogeneous elliptical inclusions with partial differential equations
- A polynomial conjecture connected with rogue waves in the KdV equation
- Inverse boundary value problem for a fractional differential equations of mixed type with integral redefinition conditions
- Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method
- An attractive numerical algorithm for solving nonlinear Caputo–Fabrizio fractional Abel differential equation in a Hilbert space
- Exploring the unknown: the work of Louis Nirenberg on partial differential equations
- Bifurcation of new optical solitary wave solutions for the nonlinear long-short wave interaction system via two improved models of ( G ′ G ) expansion method
- Partial differential equations in anisotropic Musielak-Orlicz spaces
- On nonlinear pantograph fractional differential equations with Atangana–Baleanu–Caputo derivative
- Optimal control of nonlinear time-delay fractional differential equations with Dickson polynomials
- Refraction simulation of internal solitary waves for the fractional Benjamin–Ono equation in fluid dynamics
- A novel homotopy perturbation method with applications to nonlinear fractional order KdV and Burger equation with exponential-decay kernel
- Nonlinear parabolic stochastic evolution equations in critical spaces Part I. Stochastic maximal regularity and local existence
- Numerical solution of fractional partial differential equations via Haar wavelet
- Functional inequalities: nonlinear flows and entropy methods as a tool for obtaining sharp and constructive results
- New variational theory for coupled nonlinear fractal Schrödinger system
- The impact of LRBF-FD on the solutions of the nonlinear regularized long wave equation
- A convex optimization framework for the inverse problem of identifying a random parameter in a stochastic partial differential equation
- The effect of multiplicative noise on the exact solutions of nonlinear Schrödinger equation
- Lie symmetries, exact solutions, and conservation laws of the nonlinear time-fractional Benjamin-Ono equation
- Heat transfer of TiO2− EG nanoliquid with active and passive control of nanoparticles subject to nonlinear Boussinesq approximation
- A ring vibration isolator enhanced by a nonlinear energy sink
- Dynamics of optical solitons and nonautonomous complex wave solutions to the nonlinear Schrodinger equation with variable coefficients
- Best approximation of a nonlinear fractional Volterra integro-differential equation in matrix MB-space
- Accurate sets of solitary solutions for the quadratic–cubic fractional nonlinear Schrödinger equation
- Exact solutions of the KdV equation with dual-power law nonlinearity
- Optical solitons of the resonant nonlinear Schrödinger equation with arbitrary index
- Dynamical behaviour of Chiral nonlinear Schrödinger equation
- A generalized operational matrix of mixed partial derivative terms with applications to multi-order fractional partial differential equations
- A popular reaction-diffusion model fractional Fitzhugh-Nagumo equation: analytical and numerical treatment
- On the Solvability of One Class of Third-Order Differential Equations
- Abundant analytical solutions to the new coupled Konno-Oono equation arising in magnetic field
- Numerical treatment of multi-term time fractional nonlinear KdV equations with weakly singular solutions
- Blow-up result for a semilinear wave equation with a nonlinear memory term
- An approximation technique for first Painlevé equation
- DeepXDE: A deep learning library for solving differential equations
- Some important criteria for oscillation of non-linear differential equations with middle term
- … numerical method based on shifted fractional-order Jacobi operational matrices for solving some classes of two-dimensional nonlinear fractional integral equations
- Solving nonlinear differential equations with differentiable quantum circuits
- Bäcklund transformation, exact solutions and diverse interaction phenomena to a (3+ 1)-dimensional nonlinear evolution equation
- Nonlinear instability of two streaming-superposed magnetic Reiner-Rivlin Fluids by He-Laplace method
- A spectral approach to analyze the nonlinear oscillatory fractional-order differential equations
- Employing Hirota’s bilinear form to find novel lump waves solutions to an important nonlinear model in fluid mechanics
- Applications of a fixed point result for solving nonlinear fractional and integral differential equations
- Investigation of magneto-electro-thermo-mechanical loads on nonlinear forced vibrations of composite cylindrical shells
- Inverse problem of recovering the initial condition for a nonlinear equation of the reaction–diffusion–advection type by data given on the position of a reaction front with …
- Dynamics and exact solutions of non-evolutionary partial differential equations
- On a Volterra type fractional integro-differential equation with degenerate kernel
- Distribution dependent stochastic differential equations
- Boundary value problem in a domain with deviation from the characteristics for one nonlinear equation of a mixed type
- Comparison of Finite-Difference Schemes for the Burgers Problem
- The analysis of fractional-order proportional delay physical models via a novel transform
- A self-adjoint coupled system of nonlinear ordinary differential equations with nonlocal multi-point boundary conditions on an arbitrary domain
- New analytical solitary and periodic wave solutions for generalized variable-coefficients modified KdV equation with external-force term presenting …
- Advanced Numerical Methods for Differential Equations: Applications in Science and Engineering
- Boundary value problem for a fully nonlinear elliptic equation
- New optical solitons perturbation in the birefringent fibers for the CGL equation with Kerr law nonlinearity using two integral schemes methods
- Study on the training model of football movement trajectory drop point based on fractional differential equation
- Dynamics of a D’Alembert wave and a soliton molecule for an extended BLMP equation
- Solving forward and inverse problems of the nonlinear Schrödinger equation with the generalized-symmetric Scarf-II potential via PINN deep learning
- An application of Genocchi wavelets for solving the fractional Rosenau-Hyman equation☆
- Numerical solution for multi-term fractional delay differential equations
- Solution of wave equation by Double Laplace and Double Sumudu transform
- Qualitative analysis of Caputo fractional integro-differential equations with constant delays
- To study existence of at least three weak solutions to a system of over-determined Fredholm fractional integro-differential equations
- Numerical treatment of a fractional order system of nonlinear stochastic delay differential equations using a computational scheme
- Analytical solutions to the M-derivative resonant Davey–Stewartson equations
- Asymptotic behavior of nonlocal partial differential equations with long time memory
- Fractional simulation for Darcy-Forchheimer hybrid nanoliquid flow with partial slip over a spinning disk
- Some exact wave solutions to a variety of the Schrödinger equation with two nonlinearity laws and conformable derivative
- Inverse differential quadrature method: mathematical formulation and error analysis
- Dynamics of lump-periodic and breather waves solutions with variable coefficients in liquid with gas bubbles
- Local symmetry structure and potential symmetries of time-fractional partial differential equations
- The bright and singular solitons of (2+ 1)-dimensional nonlinear Schrödinger equation with spatio-temporal dispersions
- Equivalent finite difference and partial differential equations for the lattice Boltzmann method
- An exploratory study on machine learning to couple numerical solutions of partial differential equations
- Error estimation for second-order partial differential equations in nonvariational form
- A comparison of automatic differentiation and continuous sensitivity analysis for derivatives of differential equation solutions
- Effects of fractional order time derivative on the solitary wave dynamics of the generalized ZK–Burgers equation
- Spectral methods for nonlinear functionals and functional differential equations
- Ordinary differential equations and generalized functions
- Double-diffusive natural convective stream due to moving vertical plate with nonlinear thermal radiation and Newton’s boundary constraint
- On the Formulaic Solution of a ( n + 1 ) th Order Differential Equation
- New conservation laws and exact solutions of the special case of the fifth-order KdV equation
- Computational Simulations; Abundant Optical Wave Solutions Atangana Conformable Fractional Nonlinear Schrödinger Equation
- On the boundary value problems of Hadamard fractional differential equations of variable order via Kuratowski MNC technique
- Explicit blowing up solutions for a higher order parabolic equation with Hessian Nonlinearity
- Analysis of transient thermal distribution in a convective–radiative moving rod using two-dimensional differential transform method with multivariate Pade approximant
- Numerical simulation of a nonlinear coupled differential system describing a convective flow of Casson gold–blood nanofluid through a stretched rotating rigid disk in …
- Informatisation of educational reform based on fractional differential equations
- Generalized squared remainder minimization method for solving multi-term fractional differential equations
- Numerical solution of the second order linear and nonlinear integro-differential equations using Haar wavelet method
- Quantum quantile mechanics: solving stochastic differential equations for generating time-series
- Nonlinear Differential Equations with Distributed Delay: Some New Oscillatory Solutions
- On the modified Gardner type equation and its time fractional form
- Nonlinear discrete fractional sum inequalities related to the theory of discrete fractional calculus with applications
- Solve fractional differential equations via a hybrid method between variational iteration method and gray wolf optimization algorithm
- An encyclopedia of Kudryashov’s integrability approaches applicable to optoelectronic devices
- Optical soliton solutions for the coupled conformable Fokas–Lenells equation with spatio-temporal dispersion
- A new computational method based on fractional Lagrange functions to solve multi-term fractional differential equations
- An efficient stochastic numerical computing framework for the nonlinear higher order singular models
- On some novel solution solutions to the generalized Schrödinger-Boussinesq equations for the interaction between complex short wave and real long wave …
- Computational examination of Casson nanofluid due to a non-linear stretching sheet subjected to particle shape factor: Tiwari and Das model
- Nonlinear fractional mathematical model of tuberculosis (TB) disease with incomplete treatment under Atangana-Baleanu derivative
- Analysis of Time-Fractional ϕ 4 -Equation with Singular and Non-Singular Kernels
- … wave solution to the time-fractional phi-four and (2+ 1) dimensional CBS equations using the modified extended tanh-function method in mathematical …
- Nonlinear diffusion equation with selective source for binarization of degraded document images
- Lump solutions to a (2+ 1)-dimensional fourth-order nonlinear PDE possessing a Hirota bilinear form
- Periodic-soliton and periodic-type solutions of the (3+ 1)-dimensional Boiti–Leon–Manna–Pempinelli equation by using BNNM
- The analysis of the soliton-type solutions of conformable equations by using generalized Kudryashov method
- Suppressing the vibration of the third-order critically damped Duffing equation
- Construction of an approximate analytical solution for multi-dimensional fractional Zakharov–Kuznetsov equation via Aboodh Adomian decomposition method
- Fast-diffusion limit for reaction-diffusion equations with multiplicative noise
- Soliton solutions for fractional DNA Peyrard-Bishop equation via the extended-expansion method
- New exact solutions for the doubly dispersive equation using the improved Bernoulli sub-equation function method
- New computational results for a prototype of an excitable system
- New localized and periodic solutions to a Korteweg–de Vries equation with power law nonlinearity: applications to some plasma models
- Nonlinear vibrations of functionally graded graphene reinforced composite cylindrical panels
- Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front
- Localized Chebyshev collocation method for solving elliptic partial differential equations in arbitrary 2D domains
- Solitons dynamics in optical metamaterial with quadratic–cubic nonlinearity using modified extended direct algebraic method
- An optimal Galerkin-homotopy asymptotic method applied to the nonlinear second-order bvps
- An analytical solution for nonlinear vibration analysis of functionally graded rectangular plate in contact with fluid
- Novel trial functions and rogue waves of generalized breaking soliton equation via bilinear neural network method
- Analytical behavior of the fractional Bogoyavlenskii equations with conformable derivative using two distinct reliable methods
- Heat and mass transfer analysis of the peristaltic driven flow of nanofluid in an asymmetric channel
- The Radhakrishnan–Kundu–Lakshmanan equation with arbitrary refractive index and its exact solutions
- Taylor approximation for chance constrained optimization problems governed by partial differential equations with high-dimensional random parameters
- Construction of Lump and optical solitons solutions for (3+ 1) model for the propagation of nonlinear dispersive waves in inhomogeneous media
- Two linearized schemes for time fractional nonlinear wave equations with fourth-order derivative
- Nonlinear vibration analysis of nanowire resonators for ultra-high resolution mass sensing
- A unified Petrov–Galerkin spectral method and fast solver for distributed-order partial differential equations
- A novel analytical method for solving (2+ 1)-dimensional extended Calogero-Bogoyavlenskii-Schiff equation in plasma physics
- Deep neural network for system of ordinary differential equations: Vectorized algorithm and simulation
- Can transfer neuroevolution tractably solve your differential equations?
- A novel perspective for the fractal Schrödinger equation
- On nonlinear Feynman–Kac formulas for viscosity solutions of semilinear parabolic partial differential equations
- Notes on the existence of entire solutions for several partial differential-difference equations
- The Schrödinger-KdV equation of fractional order with Mittag-Leffler nonsingular kernel
- Computational techniques to study the dynamics of generalized unstable nonlinear Schrödinger equation
- Symbolic computation and sensitivity analysis of nonlinear Kudryashov’s dynamical equation with applications
- … solitary wave solutions, bifurcation analysis and first order conserved quantities of resonance nonlinear Schrödinger’s equation with Kerr law nonlinearity
- Cerebrospinal fluid dynamics coupled to the global circulation in holistic setting: mathematical models, numerical methods and applications
- Simulation and refraction event of complex hyperbolic type solitary wave in plasma and optical fiber for the perturbed Chen-Lee-Liu equation
- Dromion− like structures in a cubic− quintic nonlinear Schrödinger equation using analytical methods
- Legendre wavelet method for fractional delay differential equations
- Soliton interaction of a generalized nonlinear Schrödinger equation in an optical fiber
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- Effects of fractional order derivative on the solution of time-fractional Cahn–Hilliard equation arising in digital image inpainting
- Propagation of dust-acoustic nonlinear waves in a superthermal collisional magnetized dusty plasma
- … transformation, Lax pair and interactions of nonlinear waves for a generalized (2+ 1)-dimensional nonlinear wave equation in nonlinear optics/fluid mechanics/plasma …
- An inverse problem for non-linear fractional magnetic schrodinger equation
- Optical bidirectional wave-solutions to new two-mode extension of the coupled KdV–Schrodinger equations
- Insight into the dynamics of Oldroyd-B fluid over an upper horizontal surface of a paraboloid of revolution subject to chemical reaction dependent on the first-order …
- Physics-informed neural networks for solving Reynolds-averaged Navier–Stokes equations
- Weak Harnack inequalities for eigenvalues and constant rank theorems
- On the representation of solutions to elliptic pdes in barron spaces
- A novel design of morlet wavelet to solve the dynamics of nervous stomach nonlinear model
- Novel approach to the analysis of fifth-order weakly nonlocal fractional Schrödinger equation with Caputo derivative
- Darcy-Forchheimer flow of dusty tangent hyperbolic fluid over a stretching sheet with Cattaneo-Christov heat flux
- Blood based hybrid nanofluid flow together with electromagnetic field and couple stresses
- Darcy-forchheimer hybrid nano fluid flow with mixed convection past an inclined cylinder
- Influence of Soret and Dufour effects on mixed convection flow over a vertical cone with injection/suction effects
- Parametric analysis of the heat transfer behavior of the nano-particle ionic-liquid flow between concentric cylinders
- Impact of stratification phenomena on a nonlinear radiative flow of sutterby nanofluid
- Numerical simulation for the mixed convective flow of non-Newtonian fluid with activation energy and entropy generation
- Stability of fractional differential equations with new generalized hattaf fractional derivative
- Numerical methods for partial differential equations
- Numerical simulation of the nonlinear fractional regularized long-wave model arising in ion acoustic plasma waves
- On heated surface transport of heat bearing thermal radiation and MHD Cross flow with effects of nonuniform heat sink/source and buoyancy opposing/assisting flow
- Quadratic residual networks: A new class of neural networks for solving forward and inverse problems in physics involving pdes
- Fractional order Alpert multiwavelets for discretizing delay fractional differential equation of pantograph type
- Some solutions for a stochastic NLSE in the unstable and higher order dispersive environments
- Conservation laws, optical molecules, modulation instability and Painlevé analysis for the Chen–Lee–Liu model
- On Solvability of a Poincare–Tricomi Type Problem for an Elliptic–Hyperbolic Equation of the Second Kind
- Thermal transport analysis in stagnation-point flow of Casson nanofluid over a shrinking surface with viscous dissipation
- Hermite multiwavelets representation for the sparse solution of nonlinear Abel’s integral equation
- Boundary value problem for a quasilinear elliptic equation with two perpendicular line of degeneration
- Numerical solutions of time fractional Zakharov-Kuznetsov equation via natural transform decomposition method with nonsingular kernel derivatives
- Numerical study of the nonlinear anomalous reaction–subdiffusion process arising in the electroanalytical chemistry
- Generalized variational principle and periodic wave solution to the modified equal width-Burgers equation in nonlinear dispersion media
- Suction and Injection Impacts on Casson Nanofluid With Gyrotactic Micro-Organisms Over a Moving Wedge
- On the approximate solutions of a class of fractional order nonlinear Volterra integro-differential initial value problems and boundary value problems of first kind and …
- Influence of radially magnetic field properties in a peristaltic flow with internal heat generation: Numerical treatment
- An operational matrix based on the Independence polynomial of a complete bipartite graph for the Caputo fractional derivative
- Study on soliton solutions of the longitudinal wave equation and magneto-electro-elastic circular rod dynamical model
- The inviscid limit of third-order linear and nonlinear acoustic equations
- Compactness of nonlinear integral operators with discontinuous and with singular kernels
- Jacobi collocation method for the fractional advection-dispersion equation arising in porous media
- Periodic solution of the time-space fractional complex nonlinear Fokas-Lenells equation by an ancient Chinese algorithm
- Knowledge-based learning of nonlinear dynamics and chaos
- Dynamics of hybrid nanofluid through a semi spherical porous fin with internal heat generation
- Invariance Analysis, Exact Solution and Conservation Laws of (2+ 1) Dim Fractional Kadomtsev-Petviashvili (KP) System
- Some dynamical models involving fractional-order derivatives with the Mittag-Leffler type kernels and their applications based upon the Legendre spectral collocation …
- Analysis of a nonstandard computer method to simulate a nonlinear stochastic epidemiological model of coronavirus-like diseases
- Novel solitary and shock wave solutions for the generalized variable-coefficients (2+ 1)-dimensional KP-Burger equation arising in dusty plasma
- Numerical investigation on unsteady MHD convective rotating flow past an infinite vertical moving porous surface
- UNIQUE SOLVABILITY OF THE BOUNDARY-VALUE PROBLEMS FOR NONLINEAR FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS
- Soliton, breather, and rogue wave solutions for solving the nonlinear Schrödinger equation using a deep learning method with physical constraints
- Micropolar fluid past a convectively heated surface embedded with nth order chemical reaction and heat source/sink
- Numerical investigation of the stagnation point flow of radiative magnetomicropolar liquid past a heated porous stretching sheet
- A granular recurrent neural network for multiple time series prediction
- Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems
- On the stability, integrability and boundedness analyses of systems of integro-differential equations with time-delay retardation
- Variational principle and approximate solution for the fractal generalized Benjamin–Bona–Mahony–Burgers equation in fluid mechanics
- Thermal analysis of a radiative slip flow of an unsteady casson nanofluid toward a stretching surface subject to the convective condition
- A unique solution of the iterative boundary value problem for a second-order differential equation approached by fixed point results
- Hybrid impact of thermal and concentration convection on peristaltic pumping of Prandtl nanofluids in non-uniform inclined channel and magnetic field
- On the nondifferentiable exact solutions to Schamel’s equation with local fractional derivative on Cantor sets
- Dynamics of lump collision phenomena to the (3+ 1)-dimensional nonlinear evolution equation
- New numerical scheme with Newton polynomial: theory, methods, and applications
- Bioconvection in a convectional nanofluid flow containing gyrotactic microorganisms over an isothermal vertical cone embedded in a porous surface with chemical …
- Unconditionally optimal error estimates of BDF2 Galerkin method for semilinear parabolic equation
- Numerical solving of the generalized Black-Scholes differential equation using Laguerre neural network
- On some novel optical wave solutions to the paraxial M-fractional nonlinear Schrödinger dynamical equation
- A comparative analysis of the fractional-order coupled Korteweg–De Vries equations with the Mittag–Leffler law
- Oceanic studies via a variable-coefficient nonlinear dispersive-wave system in the Solar System
- Complete solution for the time fractional diffusion problem with mixed boundary conditions by operational method
- Significant involvement of double diffusion theories on viscoelastic fluid comprising variable thermophysical properties
- Some novel integration techniques to explore the conformable M-fractional Schrödinger-Hirota equation
- Laplace Decomposition Method for Time-Fractional Fornberg-Whitham Type Equations
- Gudermannian neural networks using the optimization procedures of genetic algorithm and active set approach for the three-species food chain nonlinear …
- A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers’ partial differential equation
- Comparison between the new exact and numerical solutions of the Mikhailov–Novikov–Wang equation
- Generic differential equations are strongly minimal
- Soliton solutions of high-order nonlinear Schrödinger equations with different laws of nonlinearities
- Sensitive visualization of the fractional Wazwaz-Benjamin-Bona-Mahony equation with fractional derivatives: A comparative analysis
- Wave behaviors of Kundu–Mukherjee–Naskar model arising in optical fiber communication systems with complex structure
- Three-dimensional water-based magneto-hydrodynamic rotating nanofluid flow over a linear extending sheet and heat transport analysis: A numerical approach
- Nonlocal symmetries and new interaction waves of the variable-coefficient modified Korteweg–de Vries equation in fluid-filled elastic tubes
- Abundant novel wave solutions of nonlinear Klein–Gordon–Zakharov (KGZ) model
- A Maxwell’s equations based deep learning method for time domain electromagnetic simulations
- Compact implicit difference approximation for time-fractional diffusion-wave equation
- Novel analytical cnoidal and solitary wave solutions of the Extended Kawahara equation
- Summability of formal solutions for some generalized moment partial differential equations
- Global existence and decay estimates of energy of solutions for a new class of-Laplacian heat equations with logarithmic nonlinearity
- Bifurcation and new exact traveling wave solutions to time-space coupled fractional nonlinear Schrödinger equation
- Initial value problem for fractional Volterra integrodifferential pseudo-parabolic equations
- Double Mahgoub transform for the solution of parabolic boundary value problems
- Nonlinear forced vibration of in-plane bi-directional functionally graded materials rectangular plate with global and localized geometrical imperfections
- Fractional residual series for conformable time-fractional Sawada–Kotera–Ito, Lax, and Kaup–Kupershmidt equations of seventh order
- Thermal charactristics for the flow of Williamson hybrid nanofluid (MoS2+ ZnO) based with engine oil over a streched sheet
- Bioconvection: Significance of mixed convection and mhd on dynamics of Casson nanofluid in the stagnation point of rotating sphere via finite element simulation
- Arbitrary Global Lie Group Actions on Generalised Solutions of Nonlinear PDEs and an Answer to Hilbert’s Fifth Problem
- A brief review of numerical methods for heat and mass transfer of Casson fluids
- Heat transport investigation of hybrid nanofluid (Ag-CuO) porous medium flow: Under magnetic field and Rosseland radiation
- A note on the nonexistence of global solutions to the semilinear wave equation with nonlinearity of derivative-type in the generalized Einstein-de Sitter spacetime
- Variational system identification of the partial differential equations governing microstructure evolution in materials: Inference over sparse and spatially unrelated data
- Lie symmetry analysis of a stochastic gene evolution in double-chain deoxyribonucleic acid system
- A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions
- Hybrid FEM-NN models: Combining artificial neural networks with the finite element method
- Mathematics of wave propagation
- Regularization of the backward solution of parabolic problems