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SIGMA, 2012, Volume 8, 051, 5 pages (Mi sigma728)  

This article is cited in 6 scientific papers (total in 6 papers)

A two-component generalization of the integrable rdDym equation

Oleg I. Morozov

Institute of Mathematics and Statistics, University of Tromsø, Tromsø 90-37, Norway

Abstract: We find a two-component generalization of the integrable case of rdDym equation. The reductions of this system include the general rdDym equation, the Boyer–Finley equation, and the deformed Boyer–Finley equation. Also we find a Bäcklund transformation between our generalization and Bodganov's two-component generalization of the universal hierarchy equation.

Keywords: coverings of differential equations, Bäcklund transformations.

DOI: https://doi.org/10.3842/SIGMA.2012.051

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Full text: http://emis.mi.ras.ru/.../051
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Bibliographic databases:

ArXiv: 1205.1149
MSC: 35A30; 58H05; 58J70
Received: May 26, 2012; in final form August 9, 2012; Published online August 11, 2012
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Citation: Oleg I. Morozov, “A two-component generalization of the integrable rdDym equation”, SIGMA, 8 (2012), 051, 5 pp.

Citation in format AMSBIB
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\by Oleg I. Morozov
\paper A two-component generalization of the integrable rdDym equation
\jour SIGMA
\yr 2012
\vol 8
\papernumber 051
\totalpages 5
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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. H. Baran, I. S. Krasil'shchik, O. I. Morozov, P. Vojčák, “Coverings over Lax integrable equations and their nonlocal symmetries”, Theoret. and Math. Phys., 188:3 (2016), 1273–1295  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. K. Prykarpatski, O. E. Hentosh, Ya. A. Prykarpatsky, “Geometric structure of the classical Lagrange–d’Alembert principle and its application to integrable nonlinear dynamical systems”, 5, no. 4, 2017, 75  crossref  zmath  isi  scopus
    3. O. E. Hentosh, Ya. A. Prykarpatsky, D. Blackrnore, A. K. Prykarpatski, “Lie-algebraic structure of Lax–Sato integrable heavenly equations and the Lagrange–d’Alembert principle”, J. Geom. Phys., 120 (2017), 208–227  crossref  mathscinet  zmath  isi  scopus
    4. O. I. Morozov, M. V. Pavlov, “Backlund transformations between four Lax-integrable 3D equations”, J. Nonlinear Math. Phys., 24:4 (2017), 465–468  crossref  mathscinet  isi  scopus
    5. Ya. A. Prykarpatskyy, A. M. Samoilenko, “Classical M. A. Buhl problem, its Pfeiffer–Sato solutions, and the classical Lagrange–d’Alembert principle for the integrable heavenly-type nonlinear equations”, Ukr. Math. J., 69:12 (2018), 1924–1967  crossref  mathscinet  isi  scopus
    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  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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