A Recursion Operator for the Universal Hierarchy Equation via Cartan's Method of Equivalence

TL;DR

This paper uses Cartan's method of equivalence to derive a recursion operator for the universal hierarchy equation, enabling systematic generation of symmetries.

Contribution

It introduces a novel application of Cartan's method to obtain a recursion operator for the universal hierarchy equation.

Findings

Derived a Bäcklund autotransformation for the tangent covering

Established a recursion operator for symmetries

Enhanced understanding of the equation's symmetry structure

Abstract

We apply Cartan's method of equivalence to find a B\"acklund autotransformation for the tangent covering of the universal hierarchy equation. The transformation provides a recursion operator for symmetries of this equation.