Ring-type singular solutions of the biharmonic nonlinear Schrödinger equation

G. Baruch*, G. Fibich, E. Mandelbaum

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We present new singular solutions of the biharmonic nonlinear Schrödinger equation (NLS) it (t, x) - δ2 + ||2s = 0, x Rd , 4/d σ s σ 4. These solutions collapse with the quasi-self-similar ring profile QB , where QB (t, r)| ̃ 1 L2/s (t) QB σ r - rmax(t) L(t) δ , r= |x|, L(t) is the ring width that vanishes at singularity, rmax(t) ̃ r0La(t) is the ring radius, and a = (4 - s)/(s (d - 1)). The blowup rate of these solutions is 1/(3 + a) for 4/d σ s < 4, and slightly faster than 1/4 for s = 4. These solutions are analogous to the ring-type solutions of the NLS.

Original languageEnglish
Pages (from-to)2867-2887
Number of pages21
JournalNonlinearity
Volume23
Issue number11
DOIs
StatePublished - Nov 2010

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