Radiation From a Sine-Gordon Soliton Propagating in an External Potential

TL;DR

This paper investigates how a sine-Gordon soliton interacts with an external periodic potential, focusing on the resulting radiation emission and the relativistic dynamics of the soliton's position.

Contribution

It introduces a relativistic equation of motion for the soliton's position in an external potential and analyzes the radiation emitted during the interaction.

Findings

Radiation emission depends on the external potential.

Derived a potential-dependent evolution equation for fluctuations.

Relativistic effects are significant in soliton dynamics.

Abstract

The interaction of a fast moving sine-Gordon soliton with an external periodic potential is examined. The resulting equation of motion for the collective coordinate representing the position of the soliton is given in relativistic form. We examine the radiation emitted due to the interaction of the soliton with the potential and we calculate the potential dependent part of the time evolution equation for the creation and annihilation operators for fluctuations.