Non-Abelian covering and new recursion operators for the 4D Mart\'inez Alonso-Shabat equation

TL;DR

This paper introduces new recursion operators for the 4D Marte9nez Alonso-Shabat equation's symmetries, revealing novel symmetries through a non-Abelian covering derived from its Lax pair.

Contribution

It presents the first construction of non-Abelian coverings and new recursion operators for the 4D Marte9nez Alonso-Shabat equation, expanding the understanding of its symmetry structure.

Findings

New recursion operators generate previously unknown symmetries.

Construction of a non-Abelian covering using the Lax pair.

Enhanced symmetry algebra for the 4D Marte9nez Alonso-Shabat equation.

Abstract

We present new recursion operators for (shadows of nonlocal) symmetries of the 4D Mart\'inez Alonso-Shabat equation $u_{ty} = u_z u_{xy} - u_y u_{xz}$, and we show that their actions can produce new symmetries which are not contained in the Lie algebra of nonlocal symmetries presented in [I.S.Krasil'shchik, P.Voj\v{c}\'{a}k, On the algebra of nonlocal symmetries for the 4D Mart\'inez Alonso-Shabat equation. J. of Geom. and Phys. 163, (2021), 104122, (arXiv:2008.10281v1)]. To this end, we construct a non-Abelian covering of the equation in question using the Lax pair with two non-removable parameters.