  We investigate a (1+1)-dimensional nonlinear field theoretic model with the
field potential $V(\phi)| = |\phi|.$ 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 infinite number of degrees of freedom. The model has an interesting
scaling symmetry of the 'on shell' type. We find self-similar as well as shock
wave solutions of the field equation in that model.

High Energy Physics - Theory;Other Condensed Matter;Pattern Formation and Solitons