Interaction of topological solitons with defects: using a nontrivial   metric
  By including potential into the flat metric, we study interaction of sine-Gordon soliton with potentials. We will show numerically that while the soliton-barrier system shows fully classical behaviour, the soliton-well system demonstrates non-classical behaviour. In particular, solitons with low velocities are trapped in the well and emit energy radiation. 
Kurosh Javidan