Singular standing-ring solutions of nonlinear partial differential equations

Details Singular standing-ring solutions of nonlinear partial differential equations Singular standing-ring solutions of nonlinear partial differential equations

2009-07-12

arxiv.org/abs/0907.2016v1

Physica D: Nonlinear Phenomena, Volume 239, pp 1968-1983, 2010

Mathematics

Analysis of PDEs

34 pages, 21 figures

Scientific paper

10.1016/j.physd.2010.07.009

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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