An analytical formulation for phi^4 field-potential dynamics
  An analytical model for adding a space dependent potential to the phi^4 field is presented, by constructing a collective coordinate for solitary solution of this model. Interaction of the $\phi^{4}$ field with a delta function potential barrier and also delta function potential well is investigated. Most of the characters of the interaction are derived analytically while they are calculated by other models numerically. We will find that the behaviour of the solitary solution is like a point particle 'living' under the influence of a complicated potential which is a function of the field initial conditions and the potential parameters. 
Arash Ghahraman and Kurosh Javidan