On Shock Waves in Models with V-Shaped Potentials

Abstract

The recently found shock wave solution in the scalar field model with the field potential $V(ϕ)=|ϕ|$ is generalized to the case $V(ϕ)=|ϕ|-{1/2}λϕ^2$. We find two kinds of the shock waves, which are analogous of compression and expansion waves. The dependence of the waves on the parameter $λ$ is investigated in detail.