Group Theoretical Symmetries and Generalized Baecklund Transformations for Integrable Systems

TL;DR

This paper introduces a symmetry concept for 1+1-dimensional integrable systems that aligns with their group theoretic framework and generalizes Baecklund transformations, also addressing relativistic invariance.

Contribution

It proposes a new symmetry notion compatible with group theory and extends Baecklund transformations to broader integrable systems, including Leznov-Saveliev models.

Findings

Unified symmetry framework for integrable systems

Generalized Baecklund transformations derived

Application to relativistic invariance in Leznov-Saveliev systems

Abstract

We present a notion of symmetry for 1+1-dimensional integrable systems which is consistent with their group theoretic description and reproduces in special cases the known Baecklund transformation for the generalized Korteweg-deVries hierarchies. We also apply it to the relativistic invariance of the Leznov-Saveliev systems.