The complex sine-Gordon model on a half line

TL;DR

This paper studies the complex sine-Gordon model with boundaries, deriving boundary conditions that maintain integrability, and explores soliton solutions, boundary scattering, and bound states.

Contribution

It introduces boundary conditions for the complex sine-Gordon model that preserve integrability and analyzes classical solutions and boundary interactions.

Findings

Boundary conditions preserving integrability are derived.

Soliton and breather solutions are constructed.

Scattering and boundary bound states are analyzed.

Abstract

In this paper, we examine the complex sine-Gordon model in the presence of a boundary, and derive boundary conditions that preserve integrability. We present soliton and breather solutions, investigate the scattering of particles and solitons off the boundary and examine the existence of classical solutions corresponding to boundary bound states.