Exact solutions of semilinear radial wave equations in n dimensions
Abstract
Exact solutions are derived for an n-dimensional radial wave equation with a general power nonlinearity. The method, which is applicable more generally to other nonlinear PDEs, involves an ansatz technique to solve a first-order PDE system of group-invariant variables given by group foliations of the wave equation, using the one-dimensional admitted point symmetry groups. (These groups comprise scalings and time translations, admitted for any nonlinearity power, in addition to space-time inversions admitted for a particular conformal nonlinearity power). This is shown to yield not only group-invariant solutions as derived by standard symmetry reduction, but also other exact solutions of a more general form. In particular, solutions with interesting analytical behavior connected with blow ups as well as static monopoles are obtained.
Keywords
Cite
@article{arxiv.math-ph/0309049,
title = {Exact solutions of semilinear radial wave equations in n dimensions},
author = {Stephen C. Anco and Sheng Liu},
journal= {arXiv preprint arXiv:math-ph/0309049},
year = {2007}
}
Comments
29 pages, 1 figure. Published version with minor corrections