The sine-Gordon model in the presence of defects

TL;DR

This paper explores the integrability of the sine-Gordon model with dynamical defects, deriving Lax pairs and involutive quantities, and establishing continuity conditions to confirm its integrability.

Contribution

It applies an algebraic framework to analyze the sine-Gordon model with defects, explicitly deriving key integrability structures and sewing constraints.

Findings

Explicit Lax pairs and involutive quantities derived

Integrability confirmed via sewing constraints

Continuity conditions established for defect compatibility

Abstract

The sine-Gordon model in the presence of dynamical integrable defects is investigated. This is an application of the algebraic formulation introduced for integrable defects in earlier works. The quantities in involution as well as the associated Lax pairs are explicitly extracted. Integrability i also shown using certain sewing constraints, which emerge as suitable continuity conditions.