This article is cited in 3 papers

Asymptotic expansion of the wobbling kink

O. F. Oxtoby^a, I. V. Barashenkov<sup>b

a</sup> The Council for Scientific and Industrial Research
^b University of Cape Town

Abstract: We use the method of multiple scales to study the wobbling kink of the $\phi^4$ equation. We show that the amplitude of the wobbling decays very slowly, proportionally to $t^{-1/2}$, and the wobbler hence turns out to be an extremely long-lived object.

Keywords: $\phi^4$ equation, wobbling kink, asymptotic expansion, second-harmonic radiation.

DOI: 10.4213/tmf6370

 English version: Theoretical and Mathematical Physics, 2009, 159:3, 863–869

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