Singular standing-ring solutions of nonlinear partial differential equations
Analysis of PDEs
2010-11-29 v1
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.
Keywords
Cite
@article{arxiv.0907.2016,
title = {Singular standing-ring solutions of nonlinear partial differential equations},
author = {Guy Baruch and Gadi Fibich and Nir Gavish},
journal= {arXiv preprint arXiv:0907.2016},
year = {2010}
}
Comments
34 pages, 21 figures