Symplectic methods for the Ablowitz-Ladik model

DOI10.1016/S0096-3003(96)00019-7zbMath0870.65115OpenAlexW1965757759MaRDI QIDQ1354236

O. Diekmann

Publication date: 5 May 1997

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(96)00019-7

zbMATH Keywords

symplectic methodsAblowitz-Ladik modelcubic, nonlinear Schrödinger equation

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Applications to the sciences (65Z05)

Related Items

Symplectic and multi-symplectic methods for the nonlinear Schrödinger equation, Poisson Integrators Based on Splitting Method for Poisson Systems, Approximate preservation of quadratic first integrals by explicit Runge-Kutta methods, Numerical methods for the simulation of trapped nonlinear Schrödinger systems, On some new low storage implementations of time advancing Runge-Kutta methods, Symplectic integrators for the Ablowitz-Ladik discrete nonlinear Schrödinger equation, Numerical preservation of multiple local conservation laws, A PANORAMIC VIEW OF SOME PERTURBED NONLINEAR WAVE EQUATIONS, Multi-symplectic wavelet collocation method for the nonlinear Schrödinger equation and the Camassa-Holm equation, Unnamed Item, Geometric integrators for the nonlinear Schrödinger equation, Splitting K-symplectic methods for non-canonical separable Hamiltonian problems, Symplectic simulation of dark solitons motion for nonlinear Schrödinger equation, A numerical scheme for the simulation of blow-up in the nonlinear Schrödinger equation, A multisymplectic variational integrator for the nonlinear Schrödinger equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
• Some properties of the discrete Hamiltonian method
• Numerical experience with the nonlinear Schrödinger equation
• An investigation into the effect of product approximation in the numerical solution of the cubic nonlinear Schrödinger equation
• Runge-Kutta schemes for Hamiltonian systems
• Finite-difference solutions of a non-linear Schrödinger equation
• Formal energy of a symplectic scheme for Hamiltonian systems and its applications. I
• Numerical simulation of nonlinear Schrödinger systems: A new conservative scheme
• The symplecticity of multi-step methods
• Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators
• Methods for the Numerical Solution of the Nonlinear Schroedinger Equation
• Symplectic integration of Hamiltonian systems
• Conerservative and Nonconservative Schemes for the Solution of the Nonlinear Schrödinger Equation
• An Envelope Soliton Problem
• Finite difference discretization of the cubic Schrödinger equation
• The inverse scattering transform: Semi-infinite interval
• A Nonlinear Difference Scheme and Inverse Scattering
• An O(3,1) nonlinear sigma -model and the Ablowitz-Ladik hierarchy
• Symplectic methods for the nonlinear Schrödinger equation
• Symplectic methods for the nonlinear Schrödinger equation