Interaction of double sine-Gordon solitons with external potentials: an analytical model

TL;DR

This paper presents an analytical model for double sine-Gordon soliton interactions with external potentials, predicting behaviors like passing, trapping, and oscillation, with results validated against numerical simulations.

Contribution

It introduces a novel analytical approach using a nontrivial metric to model soliton-potential interactions in the double sine-Gordon system.

Findings

Solitons pass through barriers if velocity exceeds a critical value.

Solitons can be trapped and oscillate in potential wells.

Model predictions agree with numerical simulations.

Abstract

Interaction of Double sine-Gordon solitons with a space dependent potential wall and also a potential well has been investigated by employing an analytical model based on the collective coordinate approach. The potential has been added to the model through a suitable nontrivial metric for the background space-time. The model is able to predict most of the features of the soliton-potential interaction. It is shown that a soliton can pass through a potential barrier if its velocity is greater than a critical velocity which is a function of soliton initial conditions and also characters of the potential. It is interesting that the solitons of the double sine-Gordon model can be trapped by a potential barrier and oscillate there. This situation is very important in applied physics. Soliton-well system has been investigated using the presented model too. Analytical results also have been compared with the results of the direct numerical solutions.