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arXiv 0907.20162009-07-12math.AP

Singular standing-ring solutions of nonlinear partial differential equations

Guy Baruch, Gadi Fibich, Nir Gavish

备注：: 34 pages, 21 figures
发表信息：: Physica D: Nonlinear Phenomena, Volume 239, pp 1968-1983, 2010
DOI：: 10.1016/j.physd.2010.07.009

英文摘要：

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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