Emergence and bifurcations of Lyapunov manifolds in nonlinear wave equations

Taoufik Bakri, Hil Gaétan Ellart Meijer, Ferdinand Verhulst

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    Abstract

    Persistence and bifurcations of Lyapunov manifolds can be studied by a combination of averaging-normalization and numerical bifurcation methods. This can be extended to infinite-dimensional cases when using suitable averaging theorems. The theory is applied to the case of a parametrically excited wave equation. We find fast dynamics in a finite, resonant part of the spectrum and slow dynamics elsewhere. The resonant part corresponds with an almost-invariant manifold and displays bifurcations into a wide variety of phenomena among which are 2- and 3-tori.
    Original languageUndefined
    Article number10.1007/s00332-009-9045-2
    Pages (from-to)571-596
    Number of pages26
    JournalJournal of nonlinear science
    Volume19
    Issue number5
    DOIs
    Publication statusPublished - Oct 2009

    Keywords

    • MSC-74J30
    • MSC-35B32
    • MSC-35L70
    • MSC-37G15
    • EWI-16423
    • IR-68368
    • Bifurcations
    • Nonlinear waves
    • Resonance
    • Parametric excitation
    • METIS-264106
    • Averaging

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