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  • @article{RISC3966,
    author = {E. Kartashova and M. Bustamante},
    title = {{Resonance clustering in wave turbulent regimes: Integrable dynamics}},
    language = {english},
    abstract = {Two fundamental facts of the modern wave turbulence theory are 1) existence of power energy spectra in $k$-space, and 2) existence of ``gaps" in this spectra corresponding to the resonance clustering. Accordingly, three wave turbulent regimes are singled out: \emph{kinetic}, described by wave kinetic equations and power energy spectra; \emph{discrete}, characterized by resonance clustering; and \emph{mesoscopic}, where both types of wave field time evolution coexist. In this paper we study integrable dynamics of resonance clusters appearing in discrete and mesoscopic wave turbulent regimes. Using a novel method based on the notion of dynamical invariant we establish that some of the frequently met clusters are integrable in quadratures for arbitrary initial conditions and some others -- only for particular initial conditions. We also identify chaotic behaviour in some cases. Physical implications of the results obtained are discussed.},
    journal = {Physica A: Stat. Mech. Appl.},
    volume = {submitted},
    pages = {1--31},
    publisher = {Elsevier},
    isbn_issn = {ISSN: 0378-4371},
    year = {2010},
    refereed = {yes},
    length = {31}