摘要
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.
基金
support of the Austrian Science Foundation(FWF)under project P22943-N18”Nonlinear resonances of water waves”and in part–by the Project of Knowledge Innovation Program(PKIP)of Chinese Academy of Sciences,Grant No.KJCX2.YW.W10.E.K.is very much obliged to the organizing committee of the program”New Directions in Turbulence”(KITPC/ITP-CAS,2012)and the hospitality of Kavli ITP,Beijing,where part of this work has been accomplished.
