Dynamics of multi-kinks in the presence of wells and barriers

TL;DR

This paper investigates the complex dynamics of sine-Gordon kinks interacting with smooth wells and barriers, revealing phenomena like trapping, escape, and critical velocities through analytical and numerical methods.

Contribution

It introduces a study of smooth space-dependent potentials affecting kink dynamics, extending previous work on square-well potentials with new insights into multi-kink interactions.

Findings

Critical velocities for kink-barrier interactions determined

Kink trajectories include trapping, escape, and knock-out behaviors

Multi-kink interactions exhibit complex, trajectory-dependent dynamics

Abstract

Sine-Gordon kinks are a much studied integrable system that possesses multi-soliton solutions. Recent studies on sine-Gordon kinks with space-dependent square-well-type potentials have revealed interesting dynamics of a single kink interacting with wells and barriers. In this paper, we study a class of smooth space-dependent potentials and discuss the dynamics of one kink in the presence of different wells. We also present values for the critical velocity for different types of barriers. Furthermore, we study two kinks interacting with various wells and describe interesting trajectories such as double-trapping, kink knock-out and double-escape.