Barashenkov I V, Oxtoby O F
Department of Mathematics, University of Cape Town, Rondebosch 7701, South Africa.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 2):026608. doi: 10.1103/PhysRevE.80.026608. Epub 2009 Aug 31.
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.
我们给出了摆动扭结在摆动模式振幅下任意阶的一致渐近展开。通过匹配扭结远场和核心附近的渐近展开来描述辐射的长程行为。结果表明，摆动模式的复振幅服从一个带有非线性阻尼的简单常微分方程。我们证实了振幅的t^(-1/2)衰减定律，该定律先前是基于能量考虑得到的。
