On self-similar solutions of semilinear wave equations in higher space dimensions (Q548035)

The author analyzes self-similar solutions \[ \Phi(t,|x|)= (T-t)^{-\alpha} u\left(\frac{|x|}{T-t}\right) \] of the equation \(\Phi _{tt}-\Delta \Phi -\Phi ^p=0\), \(x\in \mathbb R^n\), where \(p>2\) is odd and \(n>3\). He finds several classes of analytic solutions labeled by a single parameter, the forms of which differ in the vicinity of the light cone. He also proposes suitable numerical methods.