Twisted symmetries and integrable systems

TL;DR

This paper explores how twisted symmetries extend the ability to detect integrability in Lagrangian systems beyond traditional symmetry methods, offering new tools for analyzing complex differential equations.

Contribution

It introduces the use of twisted symmetries as a novel approach to identify integrability in systems lacking standard symmetries.

Findings

Twisted symmetries effectively detect integrability in non-standard systems.

They can be used to find solutions to differential equations where traditional symmetries fail.

The method broadens the scope of symmetry analysis in mathematical physics.

Abstract

Symmetry properties are at the basis of integrability. In recent years, it appeared that so called "twisted symmetries" are as effective as standard symmetries in many respects (integrating ODEs, finding special solutions to PDEs). Here we discuss how twisted symmetries can be used to detect integrability of Lagrangian systems which are not integrable via standard symmetries.