Integrable partial differential equations and Lie--Rinehart algebras

TL;DR

This paper introduces a novel method for constructing Lax representations of partial differential equations using twisted extensions of Lie--Rinehart algebras, expanding the algebraic tools available for integrability analysis.

Contribution

It generalizes the construction of Lax representations by applying twisted extensions to Lie--Rinehart algebras, providing new algebraic techniques for PDE integrability.

Findings

Developed a method for Lax representation construction

Applied the technique to specific PDE examples

Extended algebraic framework for integrability analysis

Abstract

We develop the method for constructing Lax representations of PDEs via the twisted extensions of their algebras of contact symmetries by generalizing the construction to the Lie--Rinehart algebras. We present examples of application of the proposed technique.