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Exact solutions of semilinear radial wave equations in n dimensions

Stephen C. Anco·Sheng Liu
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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.

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Stephen C. Anco, Sheng Liu. 2005-04-04. Exact solutions of semilinear radial wave equations in n dimensions. https://arxiv.org/abs/math-ph/0309049

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