Scattering of Topological Solitons on Barriers and Holes of Deformed Sine-Gordon Models

TL;DR

This paper investigates how topological solitons in generalized Sine-Gordon models scatter off potential barriers and holes, revealing elastic and inelastic behaviors and how these depend on a model parameter n.

Contribution

It extends the analysis of soliton scattering to generalized models depending on an integer n, exploring their behavior beyond the standard Sine-Gordon case.

Findings

Scattering on barriers is highly elastic across models.

Scattering on holes is inelastic and can cause reflection.

Critical velocity for transmission varies with n, lowest at n=3.

Abstract

We study scattering properties of topological solitons in two classes of models, which are generalizations of the Sine-Gordon model and which have recently been proposed by Bazeia et al. These two classes of models depend on an integer parameter n which, when n=2(for the first class) and n=1 (for the second class), reduce to the Sine-Gordon model. 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.