On fully-nonlinear symmetry-integrable equations with rational functions in their highest derivative: Recursion operators

TL;DR

This paper introduces a class of third-order evolution equations in 1+1 dimensions that are symmetry-integrable, characterized by explicit second-order recursion operators containing specific adjoint symmetries.

Contribution

It explicitly constructs recursion operators for a new class of symmetry-integrable equations with rational functions in their highest derivatives.

Findings

Recursion operators are explicitly derived for the class.

The equations admit second-order recursion operators with adjoint symmetries.

The class extends known integrable equations with rational functions.

Abstract

We report a class of symmetry-intergable third-order evolution equations in 1+1 dimensions under the condition that the equations admit a second-order recursion operator that contains an adjoint symmetry (integrating factor) of order six. The recursion operators are given explicitly.