Multisymplectic integration of N-coupled nonlinear Schrödinger equation with destabilized periodic wave solutions

DOI10.1016/j.chaos.2008.03.011zbMath1198.37113OpenAlexW2077574028MaRDI QIDQ602379

Ayhan Aydin

Publication date: 4 November 2010

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2008.03.011

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items

Exponential time differencing Crank-Nicolson method with a quartic spline approximation for nonlinear Schrödinger equations ⋮ A semi-explicit multi-symplectic splitting scheme for a 3-coupled nonlinear Schrödinger equation ⋮ Compact and efficient conservative schemes for coupled nonlinear <scp>S</scp>chrödinger equations ⋮ Numerical solution of coupled nonlinear Schrödinger equations on unbounded domains ⋮ Optimal error estimates of SAV Crank-Nicolson finite element method for the coupled nonlinear Schrödinger equation ⋮ Exponential time differencing schemes for the 3-coupled nonlinear fractional Schrödinger equation ⋮ Structure preserving -- field directional splitting difference methods for nonlinear Schrödinger systems ⋮ An attempt to give exact solitary and periodic wave polynomial solutions to the nonlinear Klein-Gordon-Schrödinger equations ⋮ Higher order exponential time differencing scheme for system of coupled nonlinear Schrödinger equations ⋮ Multi-symplectic splitting method for the coupled nonlinear Schrödinger equation ⋮ Lobatto IIIA-IIIB discretization of the strongly coupled nonlinear Schrödinger equation ⋮ Conservative local discontinuous Galerkin methods for a generalized system of strongly coupled nonlinear Schrödinger equations. ⋮ Efficient exponential time-differencing methods for the optical soliton solutions to the space-time fractional coupled nonlinear Schrödinger equation ⋮ Decoupled local/global energy-preserving schemes for the \(N\)-coupled nonlinear Schrödinger equations

Cites Work

• Unnamed Item
• Unnamed Item
• On the preservation of phase space structure under multisymplectic discretization
• Multi-symplectic methods for the coupled 1D nonlinear Schrödinger system
• Symplectic and multi-symplectic methods for coupled nonlinear Schrödinger equations with periodic solutions
• Compression, splitting and switching of bright and dark solitons in nonlinear directional coupler
• A survey on symplectic and multi-symplectic algorithms
• Stability of plane wave solutions of nonlinear systems
• A study on linear and nonlinear Schrödinger equations by the variational iteration method
• To the integrability of the system of two coupled nonlinear Schrödinger equations
• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• Multisymplectic schemes for the nonlinear Klein-Gordon equation.
• Backward error analysis for multi-symplectic integration methods
• Multisymplectic box schemes and the Korteweg-de Vries equation.
• Coupled-mode envelope solitary waves in a pair of cubic Schrödinger equations with cross modulation: Analytical solution and collisions with application to Rossby waves
• Stability and long time evolution of the periodic solutions to the two coupled nonlinear Schrödinger equations
• Symplectic and multi-symplectic methods for the nonlinear Schrödinger equation
• The evolution of periodic waves of the coupled nonlinear Schrödinger equations
• Numerical study of the soliton waves of the coupled nonlinear Schrödinger system
• On the solution of multicomponent nonlinear Schrödinger equations
• Cnoidal and solitary wave solutions of the coupled higher order nonlinear Schrödinger equation in nonlinear optics
• On the Painlevé integrability, periodic wave solutions and soliton solutions of generalized coupled higher-order nonlinear Schrödinger equations
• Backward error analysis for multisymplectic discretizations of Hamiltonian PDEs
• A multisymplectic variational integrator for the nonlinear Schrödinger equation
• Simulating Hamiltonian Dynamics
• Multi-symplectic integration of coupled non-linear Schrödinger system with soliton solutions
• Fourth-order nonlinear evolution equation for two Stokes wave trains in deep water
• The inverse scattering transform: Semi-infinite interval
• Bilinearization of Coupled Nonlinear Schrödinger Type Equations: Integrabilty and Solitons
• Multisymplectic geometry and multisymplectic Preissmann scheme for the KdV equation
• Numerical methods for Hamiltonian PDEs
• The disintegration of wave trains on deep water Part 1. Theory
• Symplectic methods for the nonlinear Schrödinger equation
• The symplectic Evans matrix, and the instability of solitary waves and fronts
• Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity

This page was built for publication: Multisymplectic integration of N-coupled nonlinear Schrödinger equation with destabilized periodic wave solutions