A new class of integrable defects

TL;DR

This paper introduces a new, broad Lagrangian framework for integrable defects, enabling descriptions within models like Tzitzeica and sine-Gordon, and explores their relation to Bäcklund transformations and Hamiltonian structures.

Contribution

It proposes a novel Lagrangian definition of integrable defects, applicable to models previously inaccessible, and introduces new two-parameter sine-Gordon defects with fused characteristics.

Findings

Able to describe defects in Tzitzeica model

Introduces two-parameter sine-Gordon defects

Establishes links to Bäcklund transformations

Abstract

An alternative Lagrangian definition of an integrable defect is provided and analyzed. The new approach is sufficiently broad to allow a description of defects within the Tzitzeica model, which was not possible in previous approaches, and may be generalizable. New, two-parameter, sine-Gordon defects are also described, which have characteristics resembling a pair of 'fused' defects of a previously considered type. The relationship between these defects and Backlund transformations is described and a Hamiltonian description of integrable defects is proposed.