Integrable classes of a family of evolution equations

TL;DR

This paper classifies symmetry integrable classes within a family of second order nonlinear evolution equations, identifying four distinct classes and providing recursion operators, some of which are unique for certain canonical classes.

Contribution

It introduces a complete classification of symmetry integrable classes for a specific family of nonlinear evolution equations and supplies recursion operators for these classes.

Findings

Four nonequivalent symmetry integrable classes identified

Recursion operators provided for all classes

Some recursion operators are unique to certain canonical classes

Abstract

The problem of classification into symmetry integrable classes is solved for a family of second order nonlinear evolution equations labeled by arbitrary functions. Four nonequivalent symmetry integrable classes are thus obtained and the results are transformed into known integrable equations from the literature. Recursion operators are also given for all the symmetry integrable classes found, some of which are the only ones known for some of the canonical classes.