English

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

Exactly Solvable and Integrable Systems 2022-06-22 v1

Abstract

We present new recursion operators for (shadows of nonlocal) symmetries of the 4D Mart\'inez Alonso-Shabat equation uty=uzuxyuyuxzu_{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.

Keywords

Cite

@article{arxiv.2206.10530,
  title  = {Non-Abelian covering and new recursion operators for the 4D Mart\'inez Alonso-Shabat equation},
  author = {Petr Vojcak},
  journal= {arXiv preprint arXiv:2206.10530},
  year   = {2022}
}

Comments

11 pages, 2 figures