Note on scale invariance and self-similar evolution in (3+1)-dimensional   signum-Gordon model
  Several classes of self-similar, spherically symmetric solutions of relativistic wave equation with nonlinear term of the form sign(\phi) are presented. They are constructed from cubic polynomials in the scale invariant variable t/r. One class of solutions describes a process of wiping out the initial field, another an accumulation of field energy in a finite and growing region of space. 
H. Arodz, J. Karkowski and Z. Swierczynski
hep-th math-ph math.MP nlin.SI