论文标题
通常，扭结（1+1）的渐近稳定性的足够条件
A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models
论文作者
论文摘要
我们研究了（1+ 1） - 维非线性标量场理论模型\ begin \ begin {equation*} \ partial_t^2 ϕ- \ partial_x^2 ϕ+ w'（ϕ）= 0，\ quad（t quad（t quad（t quad（t quatial_x））） \ end {equation*}在潜在$ w $的一般假设下，扭结的轨道稳定性是能量参数的结果。我们的主要结果是针对给定扭结的渐近稳定性的潜在$ w $衍生了一个简单而明确的条件。此条件适用于任何静态或移动的扭结，特别是不需要对称假设。最后，在物理文献的激励下，我们将标准的应用介绍给$ p（ϕ）_2 $理论和双重正弦 - 戈登理论。
We study stability properties of kinks for the (1+1)-dimensional nonlinear scalar field theory models \begin{equation*} \partial_t^2ϕ-\partial_x^2ϕ+ W'(ϕ) = 0, \quad (t,x)\in\mathbb{R}\times\mathbb{R}. \end{equation*} The orbital stability of kinks under general assumptions on the potential $W$ is a consequence of energy arguments. Our main result is the derivation of a simple and explicit sufficient condition on the potential $W$ for the asymptotic stability of a given kink. This condition applies to any static or moving kink, in particular no symmetry assumption is required. Last, motivated by the Physics literature, we present applications of the criterion to the $P(ϕ)_2$ theories and the double sine-Gordon theory.
