We investigate self-similar solutions of evolution equation of a (1+1) dimensional real, scalar field \varphi with V-shaped field potential U(\varphi ) = | \varphi |. The equation contains a nonlinear term of the form sign(\varphi ), and it has 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.

PACS numbers: 05.45.--a, 03.50.Kk, 11.10.Lm