@Article{CiCP-10-1211,
author = {Miguel D. Bustamante and Elena Kartashova},
title = {Resonance Clustering in Wave Turbulent Regimes: Integrable Dynamics},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {5},
pages = {1211--1240},
abstract = {<p style="text-align: justify;">Two fundamental facts of the modern wave turbulence theory are 1) existence
of power energy spectra in <em>k</em>-space, and 2) existence of &quot;gaps&quot; in this spectra
corresponding to the resonance clustering. Accordingly, three wave turbulent regimes
are singled out: <em>kinetic</em>, described by wave kinetic equations and power energy spectra;<em>discrete</em>, characterized by resonance clustering; and <em>mesoscopic</em>, where both types
of wave field time evolution coexist. In this review paper we present the results on
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 show 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.110910.160211a},
url = {http://global-sci.org/intro/article_detail/cicp/7481.html}
}