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

G. Fibich*, M. Klein

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

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 iψt(t,x)+Δψ+| ψ|p-1ψ+iδ|ψ|q-1ψ=0, 0<δ≪1, is highly asymmetric with respect to the singularity time, and the post-collapse defocusing velocity of the singular core goes to infinity as the damping coefficient δ goes to zero. In the special case of the minimal-power blowup solutions of the critical NLS, the continuation is a minimal-power solution with a higher (but finite) defocusing velocity, whose magnitude increases monotonically with the nonlinear damping exponent q.

Original languageEnglish
Pages (from-to)519-527
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Volume241
Issue number5
DOIs
StatePublished - 1 Mar 2012

Funding

FundersFunder number
Israel Science Foundation

    Keywords

    • Continuation beyond the singularity
    • NLS
    • Nonlinear damping

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