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

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.Comment: 10 pages, 6 figure