Signum-Gordon wave equation and its self-similar solutions

Arodź, H.; Klimas, P.; Tyranowski, T.

Signum-Gordon wave equation and its self-similar solutions

Authors

Arodź, H.

Klimas, P.

Tyranowski, T.

Description

We investigate self-similar solutions of evolution equation of a (1+1)-dimensional field model with the V-shaped potential $U(ϕ) = | ϕ|,$ where $ϕ$ is a real scalar field. The equation contains a nonlinear term of the form $sign(ϕ)$, 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.
22 pages, 9 figures