Collective Coordinate Approach to the Dynamics of Various Soliton-Obstruction Systems

TL;DR

This paper employs the collective coordinate method to analyze how different solitons in (1+1) dimensions interact with potential barriers and holes, providing an analytical approach to their scattering behavior.

Contribution

It introduces a collective coordinate framework to approximate soliton dynamics in various models with obstructions, validating its effectiveness across multiple soliton types.

Findings

The collective coordinate approach accurately describes soliton-obstruction interactions.

The method applies to $mbda\u03c6^{4}$, deformed Sine-Gordon, and Q-ball models.

Analytical results align well with known numerical behaviors.

Abstract

Various soliton-obstruction systems have been studied from analytical perspective. We have used collective coordinate to approach the dynamics of solitons as they meet a potential obstruction in a form of square barriers and holes for three models in (1+1) dimensions, namely: $\lambda\phi^{4}$ model, deformed Sine-Gordon model, and a model that give rise to Q-ball solution. We have shown that our approximated field solution is valid enough to describe the behaviour of solitons scattering off a potential obstruction.