Non-Abelian covering and new recursion operators for the 4D Martínez Alonso-Shabat equation

Abstract

We present new recursion operators for (shadows of nonlocal) symmetries of the 4D Martínez 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.Vojčák, On the algebra of nonlocal symmetries for the 4D Martínez 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.

arXiv comment11 pages, 2 figures