Kink–antikink stripe interactions in the two-dimensional sine–Gordon equation
Kink–antikink stripe interactions in the two-dimensional sine–Gordon equation
复制标题
二维正弦 - 戈登方程中的扭结 - 反扭结条纹相互作用
DOI：
10.1016/j.cnsns.2021.106123
复制
发表时间：
2022
影响因子：
3.9
通讯作者：
Ratliff, D.J.
中科院分区：
文献类型：
--
作者：
Carretero-González, R.;Cisneros-Ake, L.A.;Decker, R.;Koutsokostas, G.N.;Frantzeskakis, D.J.;Kevrekidis, P.G.;Ratliff, D.J.
本文的主要工作是研究嵌入二维正弦戈登方程中的准一维扭结-反扭结条纹。利用变分技术，我们减少了扭结和反扭结条纹在其各自的时空依赖宽度和位置上的相互作用动力学。所得到的简化耦合方程组可以准确地描述单个扭结条纹以及两个相互作用条纹的宽度和波动动力学。除此之外，我们还讨论了两个相关的主题：扭结中心的计算识别及其数值含义，以及二维领域中单个扭结条纹横向诱导动力学的替代微扰和多尺度方法。
The main focus of the present work is to study quasi-one-dimensional kink–antikink stripes embedded in the two-dimensional sine–Gordon equation. Using variational techniques, we reduce the interaction dynamics between a kink and an antikink stripe on their respective time and space dependent widths and locations. The resulting reduced system of coupled equations is found to accurately describe the width and undulation dynamics of a single kink stripe as well as that of two interacting ones. As an aside, we also discuss two related topics: the computational identification of the kink center and its numerical implications and alternative perturbative and multiple scales approaches to the transverse direction induced dynamics for a single kink stripe in the two-dimensional realm.