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Tr. Mat. Inst. Steklova, 2018, Volume 300, Pages 158–167 (Mi tm3855)  

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

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.


DOI: https://doi.org/10.1134/S0371968518010120

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 300, 149–158

Bibliographic databases:

UDC: 517.988.67
Received: August 26, 2017

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, Tr. 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
\serial Tr. Mat. Inst. Steklova
\yr 2018
\vol 300
\pages 158--167
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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