On convergence and stability of a numerical scheme of coupled nonlinear Schrödinger equations
From MaRDI portal
Publication:2426896
DOI10.1016/j.camwa.2007.04.038zbMath1142.65074arXivmath/0611420OpenAlexW1987605104MaRDI QIDQ2426896
Publication date: 14 May 2008
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0611420
stabilityconvergencefinite difference methodnumerical examplescoupled nonlinear Schrödinger equationsCrank-Nicolson methodsoliton collisionManakov system
Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51)
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Cites Work
- Difference schemes for solving the generalized nonlinear Schrödinger equation
- Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
- Numerical integration of a coupled Korteweg-de Vries system.
- Numerical study of the soliton waves of the coupled nonlinear Schrödinger system
- An Unconditionally Stable Three-Level Explicit Difference Scheme for the Schrödinger Equation with a Variable Coefficient
- Nonlinear differential–difference equations and Fourier analysis
- A Nonlinear Difference Scheme and Inverse Scattering
- On Convergence and Stability of the Explicit Difference Method for Solution of Nonlinear Schrödinger Equations
- Highly accurate finite difference method for coupled nonlinear Schrödinger equation
- Dufort–Frankel-Type Methods for Linear and Nonlinear Schrödinger Equations
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