Signum-Gordon wave equation and its self-similar solutions

Details Signum-Gordon wave equation and its self-similar solutions Signum-Gordon wave equation and its self-similar solutions

2007-01-16

arxiv.org/abs/hep-th/0701148v1

Acta Phys.Polon.B38:3099-3118,2007

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, 9 figures

Scientific paper

We investigate self-similar solutions of evolution equation of a (1+1)-dimensional field model with the V-shaped potential $U(\phi) = | \phi |,$ where $\phi$ is a real scalar field. The equation contains a nonlinear term of the form $sign(\phi)$, and it possesses a scaling symmetry. It turns out that there are several families of the self-similar solutions with qualitatively different behaviour. We also discuss a rather interesting example of evolution with non self-similar initial data - the corresponding solution contains a self-similar component.

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