Discretization effects in the nonlinear Schrödinger equation

DOI10.1016/S0168-9274(02)00112-5zbMath1014.65071MaRDI QIDQ1861975

Gadi Fibich, Boaz Ilan

Publication date: 10 March 2003

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

numerical examplesnonlinear Schrödinger equationblowupsemidiscretizationoscillationssingularity formationNLS equationdiscretization effectsself focusingbeam collapse

Mathematics Subject Classification ID

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

Related Items (5)

Adaptivity and Blow-Up Detection for Nonlinear Evolution Problems ⋮ Ground states in spatially discrete non-linear Schrödinger models ⋮ Well-posedness of the Cauchy problem of high dimension non-isotropic fourth-order Schrödinger equations in Sobolev spaces ⋮ Localised coherent solutions of the DSI and DSII equations -- a numerical study ⋮ On the collapse arresting effects of discreteness

Cites Work

• The focusing nonlinear Schrödinger equation: Effect of the coupling to a low frequency field
• Nonlinear Schrödinger equations and sharp interpolation estimates
• A modulation method for self-focusing in the perturbed critical nonlinear Schrödinger equation
• An iterative grid redistribution method for singular problems in multiple dimensions
• On the analytical theory for stationary self-focusing of radiation
• Self-Focusing with Fourth-Order Dispersion
• Dispersive approximations in fluid dynamics
• On dispersive difference schemes. I
• Subcritical localization in the discrete nonlinear Schrodinger equation with arbitrary power nonlinearity
• Self-Focusing in the Perturbed and Unperturbed Nonlinear Schrödinger Equation in Critical Dimension
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