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

TL;DR

This paper investigates the dynamics of kink-antikink stripe interactions in the 2D sine-Gordon equation, using variational methods to derive reduced models that accurately describe their behavior and interactions.

Contribution

It introduces a variational reduction approach to model the interaction dynamics of kink-antikink stripes in two dimensions, including width and undulation behaviors.

Findings

Reduced equations accurately describe stripe width and undulation dynamics.

The approach effectively models both single and interacting kink stripes.

Discussion includes computational and perturbative methods for kink dynamics.

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 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.