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Teoreticheskaya i Matematicheskaya Fizika, 2017, Volume 192, Number 1, Pages 23–40
DOI: https://doi.org/10.4213/tmf9195 (Mi tmf9195) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Bifurcations in Kuramoto–Sivashinsky equations

S. A. Kashchenkoab

a Demidov Yaroslavl State University, Yaroslavl, Russia
b National Research Nuclear University "MEPhI", Moscow, Russia
Full-text PDF (542 kB) Citations (6)
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DOI: https://doi.org/10.4213/tmf9195
Abstract: We consider the local dynamics of the classical Kuramoto–Sivashinsky equation and its generalizations and study the problem of the existence and asymptotic behavior of periodic solutions and tori. The most interesting results are obtained in the so-called infinite-dimensional critical cases. Considering these cases, we construct special nonlinear partial differential equations that play the role of normal forms and whose nonlocal dynamics thus determine the behavior of solutions of the original boundary value problem.
Keywords: bifurcation, stability, normal form, singular perturbation, dynamics.
Received: 24.03.2016
English version:
Theoretical and Mathematical Physics, 2017, Volume 192, Issue 1, Pages 958–973
DOI: https://doi.org/10.1134/S0040577917070029
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. A. Kashchenko, “Bifurcations in Kuramoto–Sivashinsky equations”, TMF, 192:1 (2017), 23–40; Theoret. and Math. Phys., 192:1 (2017), 958–973
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9195
  • https://doi.org/10.4213/tmf9195
  • https://www.mathnet.ru/eng/tmf/v192/i1/p23
    • This publication is cited in the following 6 articles:
    1. S. A. Kaschenko, “Comparative dynamics of chains of coupled van der Pol equations and coupled systems of van der Pol equations”, Theoret. and Math. Phys., 207:2 (2021), 640–654  mathnet  crossref  crossref  adsnasa  isi
    2. S. A. Kashchenko, “Asymptotic behavior of rapidly oscillating solutions of the modified Camassa–Holm equation”, Theoret. and Math. Phys., 203:1 (2020), 469–482  mathnet  crossref  crossref  adsnasa  isi  elib
    3. S. A. Kaschenko, “Asymptotics of regular solutions to the Camassa–Holm problem”, Comput. Math. Math. Phys., 60:2 (2020), 258–271  mathnet  crossref  crossref  isi  elib
    4. S. A. Kashchenko, S. P. Plyshevskaya, “Local dynamics of cahn-hilliard equation”, Nonlinear Phenom. Complex Syst., 22:1 (2019), 93–97  mathscinet  isi
    5. S. P. Plyshevskaya, “Asymptotic research of local dynamics families of cahn-hilliard equations”, Izv. Vyss. Uchebn. Zaved.-Prikl. Nelineynaya Din., 27:1 (2019), 63–76  crossref  isi
    6. Ch. Dong, “Topological classification of periodic orbits in the Kuramoto-Sivashinsky equation”, Mod. Phys. Lett. B, 32:15 (2018), 1850155  crossref  mathscinet  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:68
    First page:39
     
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