Wobbling kinks in $\phi^4$ theory
Pattern Formation and Solitons
2015-05-13 v1
Abstract
We present a uniform asymptotic expansion of the wobbling kink to any order in the amplitude of the wobbling mode. The long-range behaviour of the radiation is described by matching the asymptotic expansions in the far field and near the core of the kink. The complex amplitude of the wobbling mode is shown to obey a simple ordinary differential equation with nonlinear damping. We confirm the -decay law for the amplitude which was previously obtained on the basis of energy considerations.
Cite
@article{arxiv.0907.3611,
title = {Wobbling kinks in $\phi^4$ theory},
author = {I. V. Barashenkov and O. F. Oxtoby},
journal= {arXiv preprint arXiv:0907.3611},
year = {2015}
}
Comments
9 pages in a double-column format; 1 figure. This is an extended version of our previous submission in arXiv:0812.4926