Asymptotic expansion of the wobbling kink

Abstract

The method of multiple scales is used to study the wobbling kink of the ${\varphi }^4$ equation. The amplitude of the wobbling is shown to decay very slowly, as $t^{-1/2}$, and hence the wobbler turns out to be an extremely long-lived object.

10 pages, 1 figure. Part of a talk given at the workshop "Nonlinear Physics. Theory and Experiment. V", Gallipoli (Lecce), June 12-21 (2008)