Type-II B\"acklund Transformations via Gauge Transformations

TL;DR

This paper constructs type II Backlund transformations for sine-Gordon and Tzitzeica-Bullough-Dodd models using gauge transformations, demonstrating their integrability and deriving conserved quantities and modified energies.

Contribution

It introduces a novel gauge transformation approach to derive type II Backlund transformations for specific integrable models, ensuring their conserved quantities are preserved.

Findings

Infinite conserved quantities are constructed from defect matrices.

Type II defects do not break the models' integrability.

Modified energy and momentum are derived and validated.

Abstract

The construction of type II Backlund transformation for the sine-Gordon and the Tzitzeica-Bullough-Dodd models are obtained from gauge transformation. An infinite number of conserved quantities are constructed from the defect matrices. This guarantees that the introduction of type II defects for these models does not spoil their integrability. In particular, modified energy and momentum are derived and compared with those presented in recent literature.