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arXiv · 0907.2016

Singular standing-ring solutions of nonlinear partial differential equations

Guy Baruch·Gadi Fibich·Nir Gavish
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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 Schrodinger equation, the biharmonic nonlinear Schrodinger equation, the nonlinear heat equation and the nonlinear biharmonic heat equation.

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Guy Baruch, Gadi Fibich, Nir Gavish. 2009-07-12. Singular standing-ring solutions of nonlinear partial differential equations. https://doi.org/10.1016/j.physd.2010.07.009

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