The numerical treatment of the nonlinear Schrödinger equation

DOI10.1016/0898-1221(90)90195-PzbMath0702.65096MaRDI QIDQ915415

Ali B. Shamardan

Publication date: 1990

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

stabilityfinite difference methodnonlinear Schrödinger equationcomparison with other methods

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) 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) Applications to the sciences (65Z05)

Related Items (9)

The nonlinear Schrödinger equation in the finite line ⋮ The solution of nonlinear Schrödinger equations using orthogonal spline collocation ⋮ Finite difference method with cubic spline for solving nonlinear schrödinger equation ⋮ Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method ⋮ A Tau method based on non-uniform space-time elements for the numerical simulation of solitons ⋮ A fourth-order explicit schemes for the coupled nonlinear Schrödinger equation ⋮ Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation ⋮ Solving the generalized nonlinear Schrödinger equation via quartic spline approximation ⋮ Linearly implicit methods for the nonlinear Schrödinger equation in nonhomogeneous media

Cites Work

• A numerical study of the nonlinear Schrödinger equation
• Convergence of method of lines approximations to partial differential equations
• A method for the integration in time of certain partial differential equations
• Finite-difference solutions of a non-linear Schrödinger equation
• Methods for the Numerical Solution of the Nonlinear Schroedinger Equation
• Conerservative and Nonconservative Schemes for the Solution of the Nonlinear Schrödinger Equation
• Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
• An Envelope Soliton Problem

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