Commun. Comput. Phys., 14 (2013), pp. 1094-1102.

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

Elena Kartashova 1*, Loredana Tec 2

1 IFA, J. Kepler University, Linz 4040, Austria.
2 RISC, J. Kepler University, Linz 4040, Austria.

Received 18 December 2012; Accepted (in revised version) 22 January 2013
Available online 10 May 2013


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.

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PACS: 47.10.Df, 47.10.Fg, 02.70.Dh
Key words: Resonance clusters, Hamiltonian formulation, discrete wave turbulence, NR-diagram, invariants of motion.

*Corresponding author.
Email: (E. Kartashova), (L. Tec)

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