Wobbling kinks in varphi(4) theory.
We present a uniform asymptotic expansion of the wobbling kink to any order in the amplitude of the wobbling mode. The long-range behavior 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.
Department of Mathematics, University of Cape Town, Rondebosch 7701, South Africa. igor@odette.mth.uct.ac.za
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Barashenkov
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Oxtoby