Higher symmetries of the elliptic Euler-Darboux equation

TL;DR

This paper identifies a significant subalgebra of higher symmetries for the elliptic Euler-Darboux equation by mapping it to a hyperbolic analogue and analyzing the symmetry structure and generators.

Contribution

It explicitly determines the structure and generators of the symmetry Lie algebra for the elliptic Euler-Darboux equation, including symmetries up to second order.

Findings

Identified a finitely generated subalgebra of higher symmetries.

Mapped the elliptic equation to its hyperbolic analogue for analysis.

Explicitly computed symmetries depending on second-order jets.

Abstract

We find a remarkable subalgebra of higher symmetries of the elliptic Euler-Darboux equation. To this aim we map such equation into its hyperbolic analogue already studied by Shemarulin. Taking into consideration how symmetries and recursion operators transform by this complex contact transformation, we explicitly give the structure of this Lie algebra and prove that it is finitely generated. Furthermore, higher symmetries depending on jets up to second order are explicitly computed.