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arXiv · 2206.10530

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

Petr Vojcak
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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.

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Petr Vojcak. 2022-06-21. Non-Abelian covering and new recursion operators for the 4D Mart\'inez Alonso-Shabat equation. https://arxiv.org/abs/2206.10530

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