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

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 a delta function potential well is investigated. A majority of the interactive characters are derived analytically. We find that the behavior of a solitonic solution is similar to a point particle which is moved under the influence of a complicated effective potential. The effective potential is a function of the initial field conditions and parameters of added potential. (c) 2010 American Institute of Physics. [doi:10.1063/1.3511337]