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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
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English version:
Theoretical and Mathematical Physics, 2009, 158:1, 48–60
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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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http://mi.mathnet.ru/eng/tmf6299https://doi.org/10.4213/tmf6299 http://mi.mathnet.ru/eng/tmf/v158/i1/p58
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This publication is cited in the following articles:
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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
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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
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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
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V. M. Zhuravlev, “Matrichnye funktsionalnye podstanovki dlya integriruemykh dinamicheskikh sistem i uravneniya Landau–Lifshitsa”, Nelineinaya dinam., 10:1 (2014), 35–48
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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
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