A constructive method for computing generalized Manley--Rowe constants of motion

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 \emph{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.