On the stability of the nonlinear Schrödinger equation

DOI10.1016/0021-9991(85)90007-5zbMath0589.65083OpenAlexW1980014687MaRDI QIDQ1074327

B. George

Publication date: 1985

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9991(85)90007-5

zbMATH Keywords

stabilitynonlinear Schrödinger equationrecurrenceblowupNumerical resultsanalytical instabilities

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Partial differential equations of mathematical physics and other areas of application (35Q99) Applications to the sciences (65Z05)

Related Items (11)

Stability in integrable nonlocal nonlinear equations ⋮ On nonlinear instabilities in leap-frog finite difference schemes ⋮ Analytical instability of the Klein-Gordon equation ⋮ \(B\)-spline finite element studies of the nonlinear Schrödinger equation ⋮ Numerical stability analysis of nonlinear Schrödinger equation via congruence transformation ⋮ Global spectral analysis: review of numerical methods ⋮ A Tau method based on non-uniform space-time elements for the numerical simulation of solitons ⋮ \(A\)-stable Runge-Kutta methods for semilinear evolution equations ⋮ An engineer's guide to soliton phenomena: Application of the finite element method ⋮ Pseudo-spectral solution of nonlinear Schrödinger equations ⋮ Numerical experience with the nonlinear Schrödinger equation

Cites Work

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• Numerical experience with the nonlinear Schrödinger equation
• Finite-difference solutions of a non-linear Schrödinger equation
• An explicit finite-difference scheme with exact conservation properties
• Convergence of Methods for the Numerical Solution of the Korteweg—de Vries Equation
• Product Approximation for Non-linear Problems in the Finite Element Method
• Nonlinear deep water waves: Theory and experiment
• On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
• A Simplified Galerkin Method for Hyperbolic Equations
• The disintegration of wave trains on deep water Part 1. Theory
• On the Instability of Leap-Frog and Crank-Nicolson Approximations of a Nonlinear Partial Differential Equation
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