Wobbling kinks in ${\varphi }^4$ theory

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 $t^{-1/2}$-decay law for the amplitude which was previously obtained on the basis of energy considerations.

9 pages in a double-column format; 1 figure. This is an extended version of our previous submission in arXiv:0812.4926

References in corpus (4)

• Negative radiation pressure exerted on kinks
• Creating kinks from particles
• Resonantly driven wobbling kinks
• Kinks in the Hartree approximation

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