Semi-implicit operator splitting Padé method for higher-order nonlinear Schrödinger equations

DOI10.1016/j.amc.2005.12.001zbMath1102.65093OpenAlexW2053943958MaRDI QIDQ849769

Houde Han, Zhenli Xu, Jing-Song He

Publication date: 31 October 2006

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

Full work available at URL: https://doi.org/10.1016/j.amc.2005.12.001

zbMATH Keywords

numerical experimentsfinite differenceoptical solitonscomparisons

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51)

Related Items (6)

Compact discrete gradient schemes for nonlinear Schrödinger equations ⋮ A linearly semi-implicit compact scheme for the Burgers–Huxley equation ⋮ A fourth-order explicit schemes for the coupled nonlinear Schrödinger equation ⋮ High-order compact splitting multisymplectic method for the coupled nonlinear Schrödinger equations ⋮ Splitting multisymplectic integrators for Maxwell's equations ⋮ Symplectic integrator for nonlinear high order Schrödinger equation with a trapped term

Cites Work

• Pseudo-spectral solution of nonlinear Schrödinger equations
• Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
• Compact finite difference schemes with spectral-like resolution
• Difference schemes for solving the generalized nonlinear Schrödinger equation
• Operator splitting methods for generalized Korteweg-de Vries equations
• On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
• Higher-order split-step Fourier schemes for the generalized nonlinear Schrödinger equation
• Symplectic and multi-symplectic methods for the nonlinear Schrödinger equation
• \(B\)-spline finite element studies of the nonlinear Schrödinger equation
• Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations
• A simple expression for the terms in the Baker–Campbell–Hausdorff series
• Splitting methods
• Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes

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