Recursion Operators for Multidimensional Integrable PDEs

TL;DR

This paper introduces a new method for constructing recursion operators for multidimensional integrable PDEs, utilizing first-order scalar differential operators, and demonstrates its effectiveness with examples, including two novel cases.

Contribution

The paper presents a straightforward approach to derive recursion operators for multidimensional integrable PDEs using isospectral Lax pairs, applicable with computer algebra tools, and provides new examples.

Findings

New recursion operators for scalar second-order multidimensional PDEs.

Application of the method to two previously unstudied examples.

Demonstration of the approach's simplicity and effectiveness.

Abstract

We present a novel construction of recursion operators for scalar second-order integrable multidimensional PDEs with isospectral Lax pairs written in terms of first-order scalar differential operators. Our approach is quite straightforward and can be readily applied using modern computer algebra software. It is illustrated by examples, two of which are new.