Symplectic integrators for the Ablowitz-Ladik discrete nonlinear Schrödinger equation

DOI10.1016/S0375-9601(99)00353-9zbMath0935.37053MaRDI QIDQ1966904

Constance M. Schober

Publication date: 8 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

zbMATH Keywords

symplectic structuresymplectic integratorsdiscrete nonlinear Schrödinger equationRunge-Kutta algorithms

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items

Symplectic and multi-symplectic methods for the nonlinear Schrödinger equation ⋮ Mel'nikov analysis of numerically induced chaos in the nonlinear Schrödinger equation ⋮ The Gaussian semiclassical soliton ensemble and numerical methods for the focusing nonlinear Schrödinger equation ⋮ Reduced-order modeling for Ablowitz-Ladik equation ⋮ Numerical preservation of multiple local conservation laws ⋮ Derivation of the multisymplectic Crank-Nicolson scheme for the nonlinear Schrödinger equation ⋮ Poisson integrators ⋮ New second- and fourth-order accurate numerical schemes for the nonlinear cubic Schrödinger equation ⋮ Symplectic integrators for discrete nonlinear Schrödinger systems ⋮ Symplectic wavelet collocation method for Hamiltonian wave equations ⋮ Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients ⋮ Geometric integrators for the nonlinear Schrödinger equation ⋮ A bi-Hamiltonian structure for the integrable, discrete nonlinear Schrödinger system ⋮ Splitting K-symplectic methods for non-canonical separable Hamiltonian problems ⋮ A new second-order accurate time discretization method for the nonlinear cubic Schrödinger equation ⋮ Symplectic simulation of dark solitons motion for nonlinear Schrödinger equation ⋮ A multisymplectic integrator for the periodic nonlinear Schrödinger equation ⋮ Long-Term Stability of Symmetric Partitioned Linear Multistep Methods

Cites Work

• Unnamed Item
• Unnamed Item
• Chaotic and homoclinic behavior for numerical discretizations of the nonlinear Schrödinger equation
• Almost Poisson integration of rigid body systems
• Symplectic methods for the Ablowitz-Ladik model
• Geometric integrators for classical spin systems
• The Adaptive Verlet Method
• Inexact Newton Methods
• A Nonlinear Difference Scheme and Inverse Scattering
• Sympletic Finite Difference Approximations of the Nonlinear Klein--Gordon Equation
• Symplectic methods for the nonlinear Schrödinger equation