This article is cited in 16 papers

Coverings over Lax integrable equations and their nonlocal symmetries

H. Baran^a, I. S. Krasil'shchik^b, O. I. Morozov^c, P. Vojčák<sup>a

a</sup> Mathematical Institute, Silesian University in Opava, Opava, Czech Republic
^b Independent University of Moscow, Moscow, Russia
^c Faculty of Applied Mathematics, AGH University of Science and Technology, Kraków, Poland

Abstract: We consider the three-dimensional rdDym equation $u_{ty}=u_xu_{xy}- u_yu_{xx}$. Using the known Lax representation with a nonremovable parameter and two hierarchies of nonlocal conservation laws associated with it, we describe the algebras of nonlocal symmetries in the corresponding coverings.

Keywords: partial differential equation, three-dimensional rdDym equation, nonlocal symmetry, recursion operator.

DOI: 10.4213/tmf9044

 English version: Theoretical and Mathematical Physics, 2016, 188:3, 1273–1295

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