DOI10.1016/0021-9991(84)90004-4zbMath0541.65083OpenAlexW4241085052MaRDI QIDQ794419
Thiab R. Taha, Mark J. Ablowitz
Publication date: 1984
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0021-9991(84)90004-4
Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation,
The quintic spline for solving the Korteweg-de Vries equation,
Potential splitting and numerical solution of the inverse scattering problem on the line,
Automatic algorithm for the numerical inverse scattering transform of the Korteweg-de Vries equation,
Boundary integral methods for dispersive equations, Airy flow and the modified Korteweg de Vries equation,
On the numerical solution of Fisher's equation with coefficient of diffusion term much smaller than coefficient of reaction term,
Homotopy perturbation method for fractional KdV equation,
A finite element method for extended KdV equations,
Analytical and numerical aspects of certain nonlinear evolution equations. IV: Numerical, modified Korteweg-de Vries equation,
A new operator splitting method for the numerical solution of partial differential equations,
Fully discrete galerkin methods for the korteweg-de vries equation,
Extension of the Ablowitz-Ladik method to the derivative nonlinear Schrödinger equation,
Numerical solutions for fractional KdV-Burgers equation by Adomian decomposition method,
Unconventional schemes for a class of ordinary differential equations - with applications to the Korteweg-de Vries equation,
Numerical Integrators for Dispersion-Managed KdV Equation,
An Embedded Exponential-Type Low-Regularity Integrator for mKdV Equation,
Collocation in space and time: Experience with the Korteweg-de Vries equation,
Numerical solutions and solitary wave solutions of fractional KDV equations using modified fractional reduced differential transform method,
On a "Quasi" Integrable Discrete Eckhaus Equation,
A finite difference method for the Korteweg-de Vries and the Kadomtsev-Petviashvili equations,
Approximate solution for system of differential-difference equations by means of the homotopy analysis method,
Mock-integrability and stable solitary vortices,
Single soliton and double soliton solutions of the quadratic‐nonlinear Korteweg‐de Vries equation for small and long‐times,
Unnamed Item,
Time-dependent spectral renormalization method,
Neural Galerkin schemes with active learning for high-dimensional evolution equations,
On the excitation of long nonlinear water waves by a moving pressure distribution. Part 2. Three-dimensional effects,
Generalized finite-difference time-domain method with absorbing boundary conditions for solving the nonlinear Schrödinger equation on a GPU,
Numerical methods for the generalized Zakharov system.,
Homotopy analysis method for space‐ and time‐fractional KdV equation,
High order \(C^0\)-continuous Galerkin schemes for high order PDEs, conservation of quadratic invariants and application to the Korteweg-de Vries model,
The Galerkin method for the KdV equation using a new basis of smooth piecewise cubic polynomials,
A split-step Fourier method for the complex modified Korteweg-de Vries equation.,
Interaction of solitary waves for the generalized KdV equation,
Benchmarking the propagator method for nonlinear systems: a Burgers-Korteweg-deVries equation,
Finite difference schemes for \(\frac{\partial u}{\partial t}=(\frac{\partial}{\partial x})^\alpha\frac{\delta G}{\delta u}\) that inherit energy conservation or dissipation property,
A comparative study of numerical solutions of a class of KdV equation,
Sparse identification of truncation errors,
On the stability of solitary wave solutions of the fifth-order KdV equation.,
Dissipative/conservative Galerkin method using discrete partial derivatives for nonlinear evolution equations,
An effective application of differential quadrature method based onmodified cubic B-splines to numerical solutions of the KdV equation,
Implicit spectral methods for wave propagation problems,
Numerical solution of complex modified Korteweg-de Vries equation by Petrov-Galerkin method,
A semi-discrete modified KdV equation,
Splitting methods for the nonlocal Fowler equation,
Simulations of solitons using quadratic spline finite elements,
A numerical scheme for the nonlinear Schrödinger equation,
Spectral solutions to the Korteweg-de-Vries and nonlinear schrodinger equations,
Numerov type variable mesh approximations for 1D unsteady quasi-linear biharmonic problem: application to Kuramoto-Sivashinsky equation,
A numerical energy conserving method for the DNLS equation,
Exponential finite-difference method applied to Korteweg--de Vries equation for small times,
A linearized implicit pseudo-spectral method for certain non-linear water wave equations,
A scheme with a higher-order discrete invariant for the KdV equation,
A posteriori error estimates for discontinuous Galerkin methods for the generalized Korteweg-de Vries equation,
An analytical numerical method for solving the Korteweg-de Vries equation,
Local spectral time splitting method for first- and second-order partial differential equations,
High-order compact schemes for nonlinear dispersive waves,
Numerical solution of Korteweg-de Vries equation by Galerkin B-spline finite element method,
A REDUCE package for finding conserved densities of systems of implicit difference-difference equations,
On the rate of convergence of a collocation projection of the KdV equation,
An application for the higher order modified KdV equation by decomposition method,
Generation and propagation of nonlinear tsunamis in shallow water by a moving topography,
Multisoliton solution of a class of coupled soliton equations,
Numerical solution of complex modified Korteweg-de Vries equation by collocation method,
Numerical algorithms for solutions of Korteweg-de Vries equation,
New numerical solution of the Korteweg-de Vries equation,
Closed-form modified Hamiltonians for integrable numerical integration schemes,
Modification of quintic B-spline differential quadrature method to nonlinear Korteweg-de Vries equation and numerical experiments,
Numerical simulation of the stochastic Korteweg-de Vries equation,
Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations,
A Hermite rational approximation method for the Korteweg-de Vries equation,
A fast spectral algorithm for nonlinear wave equations with linear dispersion,
A conservative spectral method for several two-dimensional nonlinear wave equations,
A comparison of Fourier pseudospectral methods for the solution of the Korteweg-de Vries equation,
A small time solutions for the Korteweg-de Vries equation,
A boundary value problem for the KdV equation: comparison of finite-difference and Chebyshev methods,
Numerical realizations of solutions of the stochastic KdV equation,
Conservative, discontinuous Galerkin–methods for the generalized Korteweg–de Vries equation,
Rapid convergence of a Galerkin projection of the KdV equation,
A numerical study of compactons,
FOURTH-ORDER NUMERICAL METHODS FOR THE COUPLED KORTEWEG–DE VRIES EQUATIONS,
An explicit and numerical solutions of the fractional KdV equation,
Operator splitting methods for generalized Korteweg-de Vries equations,
Some finite difference methods for a kind of GKdV equations,
Numerical evaluations of periodic wave solutions, integrable time discretization and their applications to the mKdV–sine-Gordon equation,
An adaptive method of lines solution of the Korteweg-de Vries equation,
Parallel implementation of the split-step and the pseudospectral methods for solving higher KdV equation,
On the long-time behaviour of soliton ensembles,
Time-dependent Duhamel renormalization method with multiple conservation and dissipation laws,
Soliton solution of some nonlinear partial differential equations and its applications in fluid mechanics,
KdV equation and computations of solitons: nonlinear error dynamics