Global solutions with asymptotic self-similar behaviour for the cubic wave equation

Abstract

We construct a two-parameter family of explicit solutions to the cubic wave equation on ${\mathbb{R}}^{1+3}$. Depending on the value of the parameters, these solutions either scatter to linear, blow-up in finite time, or exhibit a new type of threshold behaviour which we characterize precisely.

41 pages, 7 figures. v2: referee suggestions incorporated. To appear in Communications in Mathematical Physics