Analytical formulation for soliton-potential dynamics

An analytical model for the soliton-potential interaction is presented by constructing a collective coordinate for the system. Most of the characters of the interaction are derived analytically while they are calculated by other models numerically. We find that the behavior of the soliton is like a point particle living under the influence of a complicated potential, that is a function of soliton velocity and the potential parameters. The analytic model does not have a clear prediction for the islands of initial velocities in which the soliton may reflect back or escape over the potential well.