The Canonical Symmetry for Integrable Systems

TL;DR

This paper investigates the discrete nonlinear symmetries of integrable equations, demonstrating they are canonical transformations that alter conservation law densities by spatial divergences, with implications for understanding integrable systems.

Contribution

It establishes that discrete nonlinear symmetries in integrable systems are canonical transformations and analyzes their effects on conservation law densities.

Findings

Symmetries are canonical transformations.

Conservation law densities change by spatial divergences.

Examples illustrate the properties of these symmetries.

Abstract

The properties of discrete nonlinear symmetries of integrable equations are investigated. These symmetries are shown to be canonical transformations. On the basis of the considered examples, it is concluded, that the densities of the conservation laws are changed under these transformations by spatial divergencies.