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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, Number 2, Pages 54–68 (Mi ivm9330)  
This article is cited in 3 scientific papers (total in 3 papers)

Bifurcations in the generalized Korteweg–de Vries equation

S. A. Kashchenkoab, M. M. Preobrazhenskayabc

a MEPhi National Research Nuclear University, 31 Kashirskoe Highway, Moscow, 115409 Russia
b P.G. Demidov Yaroslavl State University, 14 Sovetskaya str., Yaroslavl, 150003 Russia
c Scientific Center in Chernogolovka of Russian Academy of Sciences, 9 Lesnaya str., Chernogolovka, Moscow region, 142432 Russia
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Abstract: We consider the generalized Korteweg–de Vries (KdV) equation and the Korteweg–de Vries–Burgers (KdVB) equation with boundary condition by space variable. For different values of the parameters in a sufficiently small neighborhood of the zero equilibrium state we construct the asymptotic behavior of periodic solutions and invariant tori. Separately we consider the case of the characteristic equation has a countable number of roots in the range of stability of the zero solution. In this situation we build a special nonlinear boundary-value problem, which plays the role of a normal form and determines the dynamics of the original problem.
Keywords: partial derivative differential equation, torus, normal form method, bifurcation.
Funding agency Grant number
Russian Science Foundation 14-21-00158
Received: 26.10.2016
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2018, Volume 62, Issue 2, Pages 49–61
DOI: https://doi.org/10.3103/S1066369X18020068
Bibliographic databases:
Document Type: Article
UDC: 517.988
Language: Russian
Citation: S. A. Kashchenko, M. M. Preobrazhenskaya, “Bifurcations in the generalized Korteweg–de Vries equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 2, 54–68; Russian Math. (Iz. VUZ), 62:2 (2018), 49–61
Citation in format AMSBIB
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\paper Bifurcations in the generalized Korteweg--de Vries equation
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\issue 2
\pages 54--68
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\vol 62
\issue 2
\pages 49--61
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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