Kink movement on a periodic background

TL;DR

This paper investigates the dynamics of kinks in the sine-Gordon model with periodic inhomogeneity, developing effective models that accurately replicate the original PDE behavior, including non-perturbative and relativistic regimes.

Contribution

It introduces a new ansatz and effective modeling approach that accurately captures kink behavior in inhomogeneous sine-Gordon systems across various conditions.

Findings

Effective models match PDE solutions well in non-perturbative regimes

Kink dynamics are accurately described with the proposed ansatz

Initial conditions influence model agreement

Abstract

The behavior of the kink in the sine-Gordon (sG) model in the presence of periodic inhomogeneity is studied. An ansatz is proposed that allows for the construction of a reliable effective model with two degrees of freedom. Effective models with excellent agreement with the original field-theoretic partial differential equation are constructed, including in the non-perturbative region and for relativistic velocities. The numerical solutions of the sG model describing the evolution of the kink in the presence of a barrier as well as in the case of a periodic heterogeneity under the potential additional influence of a switched bias current and/or dissipation were obtained. The results of the field equation and the effective models were compared. The effect of the choice of initial conditions in the field model on the agreement of the results with the effective model is discussed.