Asymptotic expansion of the wobbling kink

TL;DR

This paper uses the method of multiple scales to analyze the wobbling kink in the $\

Contribution

It provides a detailed asymptotic expansion showing the slow decay and long-lived nature of the wobbling kink in the $\

Findings

Wobbling amplitude decays as t^{-1/2}

Wobbler is an extremely long-lived object

Method of multiple scales effectively analyzes the phenomenon

Abstract

The method of multiple scales is used to study the wobbling kink of the $\phi^4$ 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.