Analytical formulation for soliton-potential dynamics

TL;DR

This paper develops an analytical model to describe soliton-potential interactions, capturing key behaviors and dynamics analytically, which were previously studied mainly through numerical methods.

Contribution

It introduces a collective coordinate approach to analytically model soliton interactions with potentials, providing insights into their behavior without relying solely on numerical simulations.

Findings

Soliton behaves like a point particle under a complex potential

Analytical expressions for interaction characteristics are derived

Model highlights limitations in predicting certain velocity regimes

Abstract

An analytical model for the soliton-potential interaction is presented, by constructing a collective coordinate for the system. Most of the characters of the interaction are derived analytically while they are calculated by other models numerically. We will find that the behaviour of the soliton is like a point particle living under the influence of a complicated potential which is a function of soliton velocity and the potential parameters. The analytic model does not have a clear prediction for the islands of initial velocities in which the soliton may reflect back or escape over the potential well.