Kink–antikink stripe interactions in the two-dimensional sine–Gordon equation

R. Carretero-González, L. A. Cisneros-Ake, R. Decker, G. N. Koutsokostas, D. J. Frantzeskakis, P. G. Kevrekidis, D. J. Ratliff

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number106123
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume109
DOIs
StatePublished - Jun 2022
Externally publishedYes

Keywords

  • Kink and anti-kinks
  • Kink stripes
  • Sine–Gordon equation
  • Variational approximation

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