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Reductions of the Universal Hierarchy and rdDym Equations and Their Symmetry Properties

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Abstract

We consider the equations

$${u_{yy}} = {u_y}{u_{xx}} - ({u_x} + u){u_{xy}} + {u_x}{u_{y,}}{u_{yy}} = ({u_x} + {u_y}){u_{xy}} - ({u_{xx}} + 2){u_y}$$

that arise as reductions of the universal hierarchy and rdDym equations, respectively, and describe the Lie algebras of nonlocal symmetries in the infinite-dimensional coverings naturally associated to these equations.

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Authors and Affiliations

  1. Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, Opava, 746 01, Czech Republic

    P. Holba & P. Vojčák

  2. Independent University of Moscow, B. Vlas’evskii per. 11, Moscow, 119002, Russia

    I. S. Krasil’shchik

  3. Trapeznikov Institute of Control Sciences, ul. Profsoyuznaya 65, Moscow, 117997, Russia

    I. S. Krasil’shchik

  4. Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, Kraków, 30–059, Poland

    O. I. Morozov

Authors
  1. P. Holba
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  2. I. S. Krasil’shchik
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  3. O. I. Morozov
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  4. P. Vojčák
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Corresponding author

Correspondence to P. Holba.

Additional information

Submitted by M. A. Malakhaltsev

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Holba, P., Krasil’shchik, I.S., Morozov, O.I. et al. Reductions of the Universal Hierarchy and rdDym Equations and Their Symmetry Properties. Lobachevskii J Math 39, 673–681 (2018). https://doi.org/10.1134/S1995080218050086

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  • DOI: https://doi.org/10.1134/S1995080218050086

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