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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Volume 300, Pages 158–167
DOI: https://doi.org/10.1134/S0371968518010120 (Mi tm3855) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Periodic oscillations and waves in nonlinear weakly coupled dispersive systems

N. I. Makarenkoab, Z. V. Makridinab

a Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia
b Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, pr. Lavrent'eva 15, Novosibirsk, 630090 Russia
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DOI: https://doi.org/10.1134/S0371968518010120
Abstract: Bifurcations of periodic solutions in autonomous nonlinear systems of weakly coupled equations are studied. A comparative analysis is carried out between the mechanisms of Lyapunov–Schmidt reduction of bifurcation equations for solutions close to harmonic oscillations and cnoidal waves. Sufficient conditions for the branching of orbits of solutions are formulated in terms of the Pontryagin functional depending on perturbing terms.
Funding agency Grant number
Russian Science Foundation 15-11-20013
This work is supported by the Russian Science Foundation under grant 15-11-20013.
Received: August 26, 2017
English version:
Proceedings of the Steklov Institute of Mathematics, 2018, Volume 300, Pages 149–158
DOI: https://doi.org/10.1134/S0081543818010121
Bibliographic databases:
Document Type: Article
UDC: 517.988.67
Language: Russian
Citation: N. I. Makarenko, Z. V. Makridin, “Periodic oscillations and waves in nonlinear weakly coupled dispersive systems”, Modern problems and methods in mechanics, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov, Trudy Mat. Inst. Steklova, 300, MAIK Nauka/Interperiodica, Moscow, 2018, 158–167; Proc. Steklov Inst. Math., 300 (2018), 149–158
Citation in format AMSBIB
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\paper Periodic oscillations and waves in nonlinear weakly coupled dispersive systems
\inbook Modern problems and methods in mechanics
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov
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\vol 300
\pages 158--167
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 1 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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