Non-Noether symmetries in integrable models

TL;DR

This paper explores non-Noether symmetries in integrable models like Toda, nonlinear Schrödinger, and KdV equations, showing they generate conservation laws and bi-Hamiltonian structures, enriching understanding of integrability.

Contribution

It demonstrates that non-Noether symmetries produce complete conservation laws and bi-Hamiltonian structures in key integrable models, offering new insights into their symmetries.

Findings

Non-Noether symmetries generate conservation laws in involution.

These symmetries lead to bi-Hamiltonian formulations.

Application to Toda, nonlinear Schrödinger, and KdV models.

Abstract

In the present paper the non-Noether symmetries of the Toda model, nonlinear Schodinger equation and Korteweg-de Vries equations (KdV and mKdV) are discussed. It appears that these symmetries yield the complete sets of conservation laws in involution and lead to the bi-Hamiltonian realizations of the above mentioned models.