Scaling, self-similar solutions and shock waves for V-shaped field potentials

We investigate a (1+1)-dimensional nonlinear field theoretic model with the field potential V(phi) = absolute value of phi. It can be obtained as the universal small amplitude limit in a class of models with potentials which are symmetrically V-shaped at their minima, or as a continuum limit of certain mechanical system with an infinite number of degrees of freedom. We point out that the model has an interesting scaling symmetry. One consequence of that is the existence of self-similar solutions of the corresponding field equations. We also find discontinuous solutions of shock wave type.