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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 158, Number 1, Pages 58–71
DOI: https://doi.org/10.4213/tmf6299 (Mi tmf6299) 		 
This article is cited in 14 scientific papers (total in 14 papers)

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

V. M. Zhuravlev

Ulyanovsk State University
Full-text PDF (418 kB) Citations (14)
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DOI: https://doi.org/10.4213/tmf6299
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.
Received: 11.09.2007
Revised: 25.06.2008
English version:
Theoretical and Mathematical Physics, 2009, Volume 158, Issue 1, Pages 48–60
DOI: https://doi.org/10.1007/s11232-009-0004-8
Bibliographic databases:
Language: Russian
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://www.mathnet.ru/eng/tmf6299
  • https://doi.org/10.4213/tmf6299
  • https://www.mathnet.ru/eng/tmf/v158/i1/p58
    • This publication is cited in the following 14 articles:
    1. V. M. Zhuravlev, V. M. Morozov, “Nelineinye volnovye uravneniya i usloviya sovmestnosti polinomialnykh differentsialnykh sootnoshenii”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2023, no. 2, 91–107  mathnet  crossref
    2. V. M. Zhuravlev, V. M. Morozov, “Nelineinye funktsionalnye podstanovki i preobrazovaniya dlya nelineinykh diffuzionnykh i volnovykh uravnenii”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2022, no. 2, 81–98  mathnet  crossref  mathscinet
    3. V. M. Zhuravlev, V. M. Morozov, “Predstavlenie Laksa s operatorami pervogo poryadka dlya novykh nelineinykh uravnenii tipa Kortevega - de Vriza”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2021, no. 4, 178–191  mathnet  crossref
    4. V. M. Zhuravlev, “Ob odnoi nelineinoi integriruemoi modeli vzaimodeistviya voln”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2020, no. 2, 94–108  mathnet  crossref
    5. V. M. Zhuravlev, “Mnogofunktsionalnye podstanovki i solitonnye resheniya integriruemykh nelineinykh uravnenii”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2019, no. 3, 93–119  mathnet  crossref
    6. V. M. Zhuravlev, “Solitonnye resheniya uravnenii tipa nelineinogo uravneniya Shredingera i funktsionalnye podstanovki”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2018, no. 1, 147–163  mathnet  crossref
    7. Yu. E. Anikonov, M. V. Neshchadim, “Generalized Cole–Hopf transformation”, J. Appl. Industr. Math., 12:3 (2018), 409–416  mathnet  mathnet  crossref  crossref  scopus
    8. 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
    9. V. M. Zhuravlev, “O mnogomernykh nelineinykh uravneniyakh, svyazannykh s uravneniyami Laplasa i teploprovodnosti funktsionalnymi podstanovkami”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2016, no. 4, 84–101  mathnet  crossref
    10. V. M. Zhuravlev, “Matrichnye funktsionalnye podstanovki dlya integriruemykh dinamicheskikh sistem i uravneniya Landau–Lifshitsa”, Nelineinaya dinam., 10:1 (2014), 35–48  mathnet
    11. 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
    12. V. M. Zhuravlev, D. A. Zinovev, “Integriruemye modeli dinamiki szhimaemoi sredy v sobstvennom pole tyagoteniya. Metod podstanovok Koula – Khopfa”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2012, no. 4, 174–190  mathnet
    13. 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
    14. 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
    Citing articles in Google Scholar: Russian citations, English citations
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