Transparent boundary conditions for the sine-Gordon equation:Modeling the reflectionless propagation of kink solitons on a line

TL;DR

This paper develops transparent boundary conditions for the sine-Gordon equation to enable reflectionless propagation of solitons, validated through numerical simulations showing no backscattering at domain boundaries.

Contribution

The authors derive and implement novel transparent boundary conditions for the sine-Gordon equation, facilitating reflectionless soliton transmission on a finite domain.

Findings

No backscattering observed in numerical simulations

Boundary conditions effectively allow reflectionless soliton propagation

Method applicable to finite domain simulations of sine-Gordon solitons

Abstract

We consider the reflectionless transport of sine-Gordon solitons on a line. Transparent boundary conditions for the sine-Gordon equation on a line are derived using the so-called potential approach. Our numerical implementation of these novel boundary conditions proves the absence of the backscattering in transmission of sine-Gordon solitons through the boundary of the considered finite domains.