The sine-Gordon model with integrable defects revisited

TL;DR

This paper revisits the sine-Gordon model with integrable defects, using an algebraic approach to identify conserved quantities and sewing conditions that preserve integrability.

Contribution

It introduces a new algebraic method to analyze integrable defects in the sine-Gordon model, ensuring consistency with Liouville integrability.

Findings

Identified first local integrals of motion.

Derived Lax pairs for the model.

Established sewing conditions at the defect point.

Abstract

Application of our algebraic approach to Liouville integrable defects is proposed for the sine-Gordon model. Integrability of the model is ensured by the underlying classical r-matrix algebra. The first local integrals of motion are identified together with the corresponding Lax pairs. Continuity conditions imposed on the time components of the entailed Lax pairs give rise to the sewing conditions on the defect point consistent with Liouville integrability.