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

2022/06/21 by P. Vojčák, Vojcak, Petr
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #35B06 #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #Sphingolipid Metabolism and Signaling

paper · pdf · doi:10.48550/arxiv.2206.10530

openalex publication_date 2022/06/21 · openalex created_date 2022/06/24 · openalex updated_date 2026/07/28

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.

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