Boundary Conditions in Stepwise Sine-Gordon Equation and Multi-Soliton Solutions

TL;DR

This paper explores the stepwise sine-Gordon equation with boundary conditions, revealing novel soliton interactions, including the formation of heavy and light pairs, and introduces the concept of a soliton gun.

Contribution

It introduces boundary conditions for the stepwise sine-Gordon equation and proposes the novel concept of a soliton gun involving high-velocity soliton pairs.

Findings

Relations between soliton velocities before and after collisions are derived.

Heavy and light soliton pairs can transform into each other under certain conditions.

The concept of a soliton gun producing high-velocity light pairs is proposed.

Abstract

We study the stepwise sine-Gordon equation, in which the system parameter is different for positive and negative values of the scalar field. By applying appropriate boundary conditions, we derive relations between the soliton velocities before and after collisions. We investigate the possibility of formation of heavy soliton pairs from light ones and vise versa. The concept of soliton gun is introduced for the first time; a light pair is produced moving with high velocity, after the annihilation of a bound, heavy pair. We also apply boundary conditions to static, periodic and quasi-periodic solutions.