Generalized symmetries of Burgers equation

TL;DR

This paper fully characterizes the algebra of generalized symmetries of the Burgers equation, providing explicit bases and demonstrating how key recursion operators generate the entire algebra.

Contribution

It offers the first complete description of the algebra of generalized symmetries for the Burgers equation, including explicit bases and generation methods.

Findings

Explicit basis of the symmetry algebra provided

Two recursion operators generate the entire algebra

Simplified proof using special coordinates in jet space

Abstract

Despite the number of relevant considerations in the literature, the algebra of generalized symmetries of the Burgers equation has not been exhaustively described. We fill this gap, presenting a basis of this algebra in an explicit form and proving that the two well-known recursion operators of the Burgers equation and two seed generalized symmetries, which are evolution forms of its Lie symmetries, suffice to generate this algebra. The core of the proof is essentially simplified by using the original technique of choosing special coordinates in the associated jet space.