Trapped States and bound states of a soliton in a well

The nature of the interaction of a soliton with an attractive well is elucidated using a model of two interacting point particles. The model explains the existence of trapped states at positive kinetic energy, as well as reflection by an attractive impurity. The transition from a trapped soliton state to a bound state is studied. Bound states of the soliton in a well are also found.