On self-similar solutions of semilinear wave equations in higher space dimensions

In this paper we analyze self-similar solutions of the semilinear wave equation Φ_tt − ΔΦ − Φ^p = 0 for n > 3 space dimensions. We found several classes of analytic solutions labeled by a single parameter, the form of which differ in the vicinity of the light cone. We also propose suitable numerical methods to study them.