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arXiv · 1001.4619

Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation

Guy Baruch·Gadi Fibich·Elad Mandelbaum
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Abstract

We present new singular solutions of the biharmonic nonlinear Schrodinger equation in dimension d and nonlinearity exponent 2σ+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^α, where α=(4-σ)/(σ(d-1)). The blowup rate of these solutions is 1/(3+α) for 4/d\leσ<4, and slightly faster than 1/4 for σ=4. These solutions are analogous to the ring-type solutions of the nonlinear Schrodinger equation.

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Guy Baruch, Gadi Fibich, Elad Mandelbaum. 2010-01-26. Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation. https://doi.org/10.1088/0951-7715%2F23%2F11%2F008

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