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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
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
Citation:
S. A. Kashchenko, “Bifurcations in Kuramoto–Sivashinsky equations”, TMF, 192:1 (2017), 23–40; Theoret. and Math. Phys., 192:1 (2017), 958–973
Linking options:
https://www.mathnet.ru/eng/tmf9195https://doi.org/10.4213/tmf9195 https://www.mathnet.ru/eng/tmf/v192/i1/p23
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