Collective coordinate variable for soliton-potential system in sine-Gordon model

TL;DR

This paper introduces a collective coordinate approach to analyze soliton interactions with delta function potentials in the sine-Gordon model, deriving analytical insights into their behavior as point particles influenced by an effective potential.

Contribution

The paper presents a novel collective coordinate variable for the sine-Gordon model with space-dependent potentials, enabling analytical study of soliton interactions with barriers and wells.

Findings

Solitons behave like point particles under an effective potential.

Interaction characteristics are derived analytically.

Behavior depends on initial conditions and potential parameters.

Abstract

A Collective coordinate variable for adding a space dependent potential to the sine-Gordon model is presented. Interaction of solitons with a delta function potential barrier and also delta function potential well is investigated. Most of the characters of interaction are derived analytically. We will find that the behaviour of a solitonic solution is like a point particle which is moved under the influence of a complicated effective potential. The effective potential is a function of the field initial conditions and also parameters of added potential.