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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2011, Issue 1(22), Pages 83–89 (Mi vsgtu857)  

This article is cited in 3 scientific papers (total in 3 papers)

Procedings of the 2nd International Conference "Mathematical Physics and its Applications"
Mathematical Physics

Method of general Coule–Hopf substitutions in theory of finite-dimensional dynamical systems

V. M. Zhuravlev, C. S. Obrubov

Dept. of Theoretical Physics, Ulyanovsk State University, Ulyanovsk

Abstract: We consider the results of applying the method of generic Cole–Hopf substitutions to integration of finite-dimensional dynamical systems. Dynamical systems are represented in the form of matrix ordinary differential equations with specific matrix algebra of finite dimension. The Cole–Hopf type substitutions are applied to matrix equations by using the differentiation on algebra in the form of commutator with a specific algebra element. Recurrent relations for Cole–Hopf substitutions were found. Particular cases of exactly integrable dynamical systems are presented. The algorithm of calculating the integrals of motion is shown.

Keywords: Burgers type equations, general Cole–Hopf substitution, finite–dimensional dynamical systems

DOI: https://doi.org/10.14498/vsgtu857

Full text: PDF file (477 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.28+517.958+517.957
MSC: Primary 70G60; Secondary 35Q70
Original article submitted 20/XII/2010
revision submitted – 27/II/2011

Citation: V. M. Zhuravlev, C. S. Obrubov, “Method of general Coule–Hopf substitutions in theory of finite-dimensional dynamical systems”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(22) (2011), 83–89

Citation in format AMSBIB
\Bibitem{ZhuObr11}
\by V.~M.~Zhuravlev, C.~S.~Obrubov
\paper Method of general Coule--Hopf substitutions in~theory of~finite-dimensional dynamical systems
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2011
\vol 1(22)
\pages 83--89
\mathnet{http://mi.mathnet.ru/vsgtu857}
\crossref{https://doi.org/10.14498/vsgtu857}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. V. M. Zhuravlev, “Matrichnye funktsionalnye podstanovki dlya integriruemykh dinamicheskikh sistem i uravneniya Landau–Lifshitsa”, Nelineinaya dinam., 10:1 (2014), 35–48  mathnet
    3. Yu. E. Anikonov, M. V. Neshchadim, “Generalized Cole–Hopf transformation”, J. Appl. Industr. Math., 12:3 (2018), 409–416  mathnet  crossref  crossref  elib  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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