Monotonicity properties of the blow-up time for nonlinear Schrödinger equations: numerical evidence

zbMath1156.35467arXivmath/0603107MaRDI QIDQ933114

Rémi Carles, Christophe Besse, Norbert J. Mauser, Hans Peter Stimming

Publication date: 21 July 2008

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603107

zbMATH Keywords

nonlinear opticsnonlinear Schrödinger equationsfinite time blow-upwave collapse

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Lasers, masers, optical bistability, nonlinear optics (78A60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (5)

Numerical validation of blow-up solutions of ordinary differential equations ⋮ Finite difference approximation for nonlinear Schrödinger equations with application to blow-up computation ⋮ A numerical method for solving the time fractional Schrödinger equation ⋮ On the Cauchy problem for the nonlinear Schrödinger equations with time-dependent linear loss/gain ⋮ Blow-up solutions to the nonlinear Schrödinger equation with oscillating nonlinearities

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