Singular standing-ring solutions of nonlinear partial differential equations

Guy Baruch, Gadi Fibich*, Nir Gavish

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We present a general framework for constructing singular solutions of nonlinear evolution equations that become singular on a d-dimensional sphere, where d>1. The asymptotic profile and blowup rate of these solutions are the same as those of solutions of the corresponding one-dimensional equation that become singular at a point. We provide a detailed numerical investigation of these new singular solutions for the following equations: The nonlinear Schrdinger equation iψt(t,x)+Δψ+|ψ|2σψ=0 with σ>2, the biharmonic nonlinear Schrdinger equation iψt(t,x)- Δ2ψ+|ψ|2σψ=0 with σ>4, the nonlinear heat equation ψt(t,x)-Δψ-|ψ|2σψ=0 with σ>0, and the nonlinear biharmonic heat equation ψt(t,x)+Δ2ψ- |ψ|2σψ=0 with σ>0.

Original languageEnglish
Pages (from-to)1968-1983
Number of pages16
JournalPhysica D: Nonlinear Phenomena
Volume239
Issue number20-22
DOIs
StatePublished - 15 Oct 2010

Funding

FundersFunder number
Iowa Science Foundation123/08
Ministry of Education, Culture, Sports, Science and Technology
Israel Science Foundation

    Keywords

    • Biharmonic nonlinear Schrdinger equation
    • Biharmonic nonlinear heat equation
    • Blowup
    • Nonlinear Schrdinger equation
    • Nonlinear heat equation
    • Ring

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