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A Constructive Method for Computing Generalized Manley-Rowe Constants of Motion
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作者 elena kartashova Loredana Tec 《Communications in Computational Physics》 SCIE 2013年第9期1094-1102,共9页
The Manley-Rowe constants of motion(MRC)are conservation laws written out for a dynamical systemdescribing the time evolution of the amplitudes in resonant triad.In this paper we extend the concept of MRC to resonance... The Manley-Rowe constants of motion(MRC)are conservation laws written out for a dynamical systemdescribing the time evolution of the amplitudes in resonant triad.In this paper we extend the concept of MRC to resonance clusters of any form yielding generalized Manley-Rowe constants(gMRC)and give a constructive method how to compute them.We also give details of a Mathematica implementation of this method.WhileMRC provide integrability of the underlying dynamical system,gMRC generally do not but may be used for qualitative and numerical study of dynamical systems describing generic resonance clusters. 展开更多
关键词 Resonance clusters Hamiltonian formulation discretewave turbulence NR-diagram invariants of motion
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Resonance Clustering in Wave Turbulent Regimes:Integrable Dynamics
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作者 Miguel D.Bustamante elena kartashova 《Communications in Computational Physics》 SCIE 2011年第10期1211-1240,共30页
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 ... 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:kinetic,described by wave kinetic equations and power energy spectra;discrete,characterized by resonance clustering;and mesoscopic,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. 展开更多
关键词 Resonance clustering Hamiltonian formulation wave turbulent regimes NRdiagram integrable dynamics.
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Laminated Wave Turbulence: Generic Algorithms Ⅱ
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作者 elena kartashova Alexey Kartashov 《Communications in Computational Physics》 SCIE 2007年第4期783-794,共12页
The model of laminated wave turbulence puts forth a novel computational problem–construction of fast algorithms for finding exact solutions of Diophantine equations in integers of order 10^(12) and more.The equations... The model of laminated wave turbulence puts forth a novel computational problem–construction of fast algorithms for finding exact solutions of Diophantine equations in integers of order 10^(12) and more.The equations to be solved in integers are resonant conditions for nonlinearly interacting waves and their form is defined by the wave dispersion.It is established that for the most common dispersion as an arbitrary function of a wave-vector length two different generic algorithms are necessary:(1)one-class-case algorithm for waves interacting through scales,and(2)two-class-case algorithm for waves interacting through phases.In our previous paper we described the one-class-case generic algorithm and in our present paper we present the two-classcase generic algorithm. 展开更多
关键词 Laminated wave turbulence discrete wave systems computations in integers transcendental algebraic equations complexity of algorithm.
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