Recursion operators in the cotangent covering of the rdDym equation

TL;DR

This paper introduces a general method for constructing nonlocal recursion operators for PDE symmetries, demonstrated on the cotangent covering of the 3D rdDym equation, including criteria for hereditary properties.

Contribution

It presents a new systematic approach to derive nonlocal recursion operators and applies it to a specific 3D PDE, providing explicit operators and hereditary property criteria.

Findings

Two mutually inverse recursion operators for the cotangent equation of the 3D rdDym equation

A rigorous criterion for checking the hereditary property of recursion operators

Explicit construction of nonlocal recursion operators for a class of PDEs

Abstract

We describe a general method of constructing nonlocal recursion operators for symmetries of PDEs. As an example, the cotangent equation to the 3D rdDym equation $u_{yt} = u_xu_{xy} - u_yu_{xx}$ for which two mutually inverse operators are found. The exposition includes a rigorous criterion to check the hereditary property.