Dynamics of kink train solutions in deformed Multiple sine-Gordon models

TL;DR

This paper studies how inhomogeneities affect periodic kink train solutions in deformed Multiple-sine-Gordon models, focusing on stability, deformation, and dynamics during interactions with medium defects.

Contribution

It investigates the impact of thin inhomogeneous layers on kink train solutions in deformed MsG models, including stability analysis and dynamic behavior during interactions.

Findings

Inhomogeneities cause critical deformations in kink trains.

Stability of kink chains is affected by medium defects.

Kink profiles change abruptly during interactions.

Abstract

This paper examines the effects of a thin layer of inhomogeneity on periodic solutions of the Multiple-sine-Gordon (MsG) model. We investigate the dynamics of the perturbed Double-sine-Gordon (DsG) system as a significant and more practical case of such configurations. The thin barrier acts as a potential well (potential barrier) and causes critical deformations in kink train solutions and some basic properties of the periodic solutions, such as the type of sub-kinks, their amplitude, energy and wavelength. Stability of the initial kink chain during the interaction with medium defects is analyzed using their phase diagram. Sudden changes in the profile of kink trains due to the disruption of their amplitude and wavelength are considered. The time evolution of moving kink chain solutions while interacting with medium fractures is also studied.