Self-similarity for V-shaped field potentials - further examples

Abstract

Three new models with V-shaped field potentials $U$ are considered: a complex scalar field $X$ in 1+1 dimensions with $U(X)=|X|$, a real scalar field $\Phi$ in 2+1 dimensions with $U(\Phi )=|\Phi |$, and a real scalar field $\varphi$ in 1+1 dimensions with $U{ϕ) = ϕΘ(ϕ)$ where $\Theta$ is the step function. Several explicit, self-similar solutions are found. They describe interesting dynamical processes, for example, `freezing' a string in a static configuration.

17 pages, 4 figures