Scattering of topological solitons on barriers and holes of deformed Sine–Gordon models

Abstract

We study various scattering properties of topological solitons in two classes of models, which are the generalizations of the Sine–Gordon model and which have recently been proposed by Bazeia et al. These two classes of models depend on a positive real nonzero parameter n but in this paper we consider the models only for its integer values as when n = 2 (for the first class) and n = 1 (for the second class), the model reduces to the Sine–Gordon one. We take the soliton solutions of these models (generalizations of the ‘kink’ solution of the Sine–Gordon model) and consider their scattering on potential holes and barriers. We present our results for n = 1, …, 6. We find that, like in the Sine–Gordon models, the scattering on the barrier is very elastic while the scattering on the hole is inelastic and can, at times, lead to a reflection. We discuss the dependence of our results on n and find that the critical velocity for the transmission through the hole is lowest for n = 3.