Singular standing-ring solutions of nonlinear partial differential equations
arXiv:0907.2016 · doi:10.1016/j.physd.2010.07.009
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.
34 pages, 21 figures
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