Note on scale invariance and self-similar evolution in (3+1)-dimensional signum-Gordon model
arXiv:1201.2279
Abstract
Several classes of self-similar, spherically symmetric solutions of relativistic wave equation with nonlinear term of the form sign(ϕ) 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.
14 pages, 4 figures; Acta Phys. Pol. B43 (2012), in print