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TMF, 2009, Volume 158, Number 1, Pages 58–71 (Mi tmf6299)  

This article is cited in 5 scientific papers (total in 5 papers)

The method of generalized Cole–Hopf substitutions and new examples of linearizable nonlinear evolution equations

V. M. Zhuravlev

Ulyanovsk State University

Abstract: We propose a new approach for constructing nonlinear evolution equations in matrix form that are integrable via substitutions similar to the Cole–Hopf substitution linearizing the Burgers equation. We use this new approach to find new integrable nonlinear evolution equations and their hierarchies.

Keywords: exactly integrable nonlinear equation, Burgers-type equation, Cole–Hopf substitution

DOI: https://doi.org/10.4213/tmf6299

Full text: PDF file (418 kB)
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English version:
Theoretical and Mathematical Physics, 2009, 158:1, 48–60

Bibliographic databases:

Received: 11.09.2007
Revised: 25.06.2008

Citation: V. M. Zhuravlev, “The method of generalized Cole–Hopf substitutions and new examples of linearizable nonlinear evolution equations”, TMF, 158:1 (2009), 58–71; Theoret. and Math. Phys., 158:1 (2009), 48–60

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6299
  • http://mi.mathnet.ru/eng/tmf/v158/i1/p58

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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. V. M. Zhuravlev, K. S. Obrubov, “Metod obobschennykh podstanovok Koula–Khopfa v teorii konechnomernykh nelineinykh dinamicheskikh sistem”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(22) (2011), 83–89  mathnet  crossref
    2. Zhuravlev V.M., Zinov'ev D.A., “Nonlinear waves in self-gravitating compressible fluid and generalized Cole-Hopf substitutions”, Physics of Wave Phenomena, 19:4 (2011), 313–317  crossref  adsnasa  isi  scopus  scopus
    3. A. N. Byzykchi, V. M. Zhuravlev, “Solitony i metod obobschennykh podstanovok Koula–Khopfa”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(31) (2013), 193–199  mathnet  crossref  elib
    4. V. M. Zhuravlev, “Matrichnye funktsionalnye podstanovki dlya integriruemykh dinamicheskikh sistem i uravneniya Landau–Lifshitsa”, Nelineinaya dinam., 10:1 (2014), 35–48  mathnet
    5. Zhuravlev V.M., “Models For the Dynamics of Dust-Like Matter in the Self-Gravity Field: the Method of Hydrodynamic Substitutions”, J. Exp. Theor. Phys., 125:3 (2017), 420–433  crossref  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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