Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation

Details Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation

2010-01-26

arxiv.org/abs/1001.4619v1

Nonlinearity, Volume 23, Number 11, pp. 2867, 2010

Mathematics

Analysis of PDEs

21 pages, 13 figures, research article

Scientific paper

10.1088/0951-7715/23/11/008

We present new singular solutions of the biharmonic nonlinear Schrodinger equation in dimension d and nonlinearity exponent 2\sigma+1. These solutions collapse with the quasi self-similar ring profile, with ring width L(t) that vanishes at singularity, and radius proportional to L^\alpha, where \alpha=(4-\sigma)/(\sigma(d-1)). The blowup rate of these solutions is 1/(3+\alpha) for 4/d\le\sigma<4, and slightly faster than 1/4 for \sigma=4. These solutions are analogous to the ring-type solutions of the nonlinear Schrodinger equation.

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