Periodic Oscillations and Waves in Nonlinear Weakly Coupled Dispersive Systems

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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.

Original languageEnglish
Pages (from-to)149-158
Number of pages10
JournalProceedings of the Steklov Institute of Mathematics
Volume300
Issue number1
DOIs
Publication statusPublished - 1 Jan 2018

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