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A Constructive Method for Computing Generalized Manley-Rowe Constants of Motion

Published online by Cambridge University Press:  03 June 2015

Elena Kartashova  and
Loredana Tec
Elena Kartashova*
Affiliation:
IFA, J. Kepler University, Linz 4040, Austria
Loredana Tec*
Affiliation:
RISC, J. Kepler University, Linz 4040, Austria
*
Corresponding author.Email:Elena.Kartaschova@jku.at
Email:Loredana.Tec@jku.at
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Abstract

The Manley-Rowe constants of motion (MRC) are conservation laws written out for a dynamical system describing 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. While MRC 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.

Keywords

47.10.Df47.10.Fg02.70.DhResonance clustersHamiltonian formulationdiscrete wave turbulenceNR-diagraminvariants of motion
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 4 , October 2013 , pp. 1094 - 1102
Copyright
Copyright © Global Science Press Limited 2013

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