The nonlinear Schrödinger equation in the finite line

DOI10.1016/0895-7177(94)90030-2zbMath0808.65134arXiv1301.3951OpenAlexW3101201433MaRDI QIDQ1336869

Juan I. Ramos, Francisco R. Villatoro

Publication date: 6 November 1994

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.3951

zbMATH Keywords

numerical resultsnonlinear Schrödinger equationperiodic boundary conditionsboundary layersoliton solutionsRobin conditionsCrank-Nicolson methodsfinite line

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) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Applications to the sciences (65Z05)

Related Items (3)

Spectral approximation for nonlinear time fractional Schrödinger equation on graded meshes ⋮ Variable mesh difference schemes for solving a nonlinear Schrödinger equation with a linear damping term ⋮ Interaction of spatial solitons with a localized spatially-modulated medium

Cites Work

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• An engineer's guide to soliton phenomena: Application of the finite element method
• A numerical study of the nonlinear Schrödinger equation
• Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
• The numerical treatment of the nonlinear Schrödinger equation
• The forced nonlinear Schrödinger equation
• Bäcklund transformations and their applications
• The hyperelliptic inverse scattering transform for the periodic, defocusing nonlinear Schrödinger equation
• Two boundary value problems for the Ginzburg-Landau equation
• An initial-boundary value problem for the nonlinear Schrödinger equation
• Methods for the Numerical Solution of the Nonlinear Schroedinger Equation
• Solitary waves induced by boundary motion
• Forced Nonlinear Evolution Equations and the Inverse Scattering Transform
• New Directions in Solitons and Nonlinear Periodic Waves: Polycnoidal Waves, Imbricated Solitons, Weakly Nonlocal Solitary Waves, and Numerical Boundary Value Algorithms
• Solitons induced by boundary conditions from the Boussinesq equation
• Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
• Collisions between two solitary waves. Part 2. A numerical study
• The Periodic Cubic Schrõdinger Equation
• Dynamics of Semi-Discretizations of the Defocusing Nonlinear Schrödinger Equation
• Initial boundary value problem for the nonlinear Schrodinger equation
• Finite difference discretization of the cubic Schrödinger equation
• The inverse scattering transform: Semi-infinite interval

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