Nonlinear-damping continuation of the nonlinear Schrödinger equation — A numerical study

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Mar 2012Embargo end date: 01 Jan 2011 English Publisher:Elsevier BVJournal:Physica D: Nonlinear Phenomena, volume 241, pages 519-527 (issn: 0167-2789,

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Authors: Fibich, G.; Klein, M.;

doi: 10.1016/j.physd.2011.11.008 , 10.48550/arxiv.1107.3281

arXiv: 1107.3281

Nonlinear-damping continuation of the nonlinear Schrödinger equation — A numerical study

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Abstract

We study the nonlinear-damping continuation of singular solutions of the critical and supercritical NLS. Our simulations suggest that for generic initial conditions that lead to collapse in the undamped NLS, the solution of the weakly-damped NLS $$ iψ_t(t,\X)+Δψ+|ψ|^{p-1}ψ+iδ|ψ|^{q-1}ψ=0,\qquad0

Related Organizations

Tel Aviv University
Israel
School of Mathematical Sciences Tel Aviv University
Israel

Keywords

NLS equations (nonlinear Schrödinger equations), nonlinear damping, NLS, FOS: Physical sciences, Mathematical Physics (math-ph), continuation beyond the singularity, Mathematics - Analysis of PDEs, Applications to the sciences, FOS: Mathematics, Continuation and prolongation of solutions to PDEs, Mathematical Physics, Analysis of PDEs (math.AP)

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