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 TMF, 2016, Volume 188, Number 3, Pages 361–385 (Mi tmf9044)

Coverings over Lax integrable equations and their nonlocal symmetries

H. Barana, I. S. Krasil'shchikb, O. I. Morozovc, P. Vojčáka

a 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

 Funding Agency Grant Number Simons Foundation Ministry of Science and Higher Education (Poland) The research of I. S. Krasil'shchik was supported in part by a Simons-IUM fellowship. The research of O. I. Morozov was supported by the Polish Ministry of Science and Higher Education.

DOI: https://doi.org/10.4213/tmf9044

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

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Citation: H. Baran, I. S. Krasil'shchik, O. I. Morozov, P. Vojčák, “Coverings over Lax integrable equations and their nonlocal symmetries”, TMF, 188:3 (2016), 361–385; Theoret. and Math. Phys., 188:3 (2016), 1273–1295

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf9044
• https://doi.org/10.4213/tmf9044
• http://mi.mathnet.ru/eng/tmf/v188/i3/p361

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. I. S. Krasil'shchik, A. Sergyeyev, O. I. Morozov, “Infinitely many nonlocal conservation laws for the ABC equation with
$$A+B+C\ne 0$$
”, Calc. Var. Partial Differ. Equ., 55:5 (2016), 123, 12 pp.
2. O. I. Morozov, M. V. Pavlov, “Backlund transformations between four Lax-integrable 3D equations”, J. Nonlinear Math. Phys., 24:4 (2017), 465–468
3. A. Lelito, O. I. Morozov, “Nonlocal symmetries of Plebański's second heavenly equation”, J. Nonlinear Math. Phys., 25:2 (2018), 188–197
4. A. Lelito, O. I. Morozov, “Three-component nonlocal conservation laws for Lax-integrable 3D partial differential equations”, J. Geom. Phys., 131 (2018), 89–100
5. H. Baran, I. S. Krasil'shchik, O. I. Morozov, P. Vojčák, “Nonlocal symmetries of integrable linearly degenerate equations: A comparative study”, Theoret. and Math. Phys., 196:2 (2018), 1089–1110
6. Morozov O.I., “Lax Representations With Non-Removable Parameters and Integrable Hierarchies of Pdes Via Exotic Cohomology of Symmetry Algebras”, J. Geom. Phys., 143 (2019), 150–163
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