Dynamical properties of a Soliton in a Potential Well

TL;DR

This paper investigates how a two-dimensional soliton interacts with a potential well, revealing conditions for passing, bouncing, or trapping, and highlights the importance of vibrational modes in these dynamics.

Contribution

It introduces a pseudo-geodesic model to explain the soliton's interaction with potential wells, emphasizing the role of vibrational modes in the process.

Findings

Critical velocity depends on well width and depth.

Vibrational modes significantly influence soliton dynamics.

Model accurately predicts soliton behavior in potential wells.

Abstract

We analyse the scattering of a two-dimensional soliton on a potential well. We show that this soliton can pass through the well, bounce back or become trapped and we study the dependence of the critical velocity on the width and the depth of the well. We also present a model based on a pseudo-geodesic approximation to the full system which shows that the vibrational modes of the soliton play a crucial role in the dynamical properties of its interactions with potential wells.