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Volume 14, Issue 4
A Constructive Method for Computing Generalized Manley-Rowe Constants of Motion

Elena Kartashova & Loredana Tec

DOI: 10.4208/cicp.181212.220113a

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

Published online: 2013-10

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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.

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@Article{CiCP-14-1094, author = {Elena Kartashova and Loredana Tec}, title = {A Constructive Method for Computing Generalized Manley-Rowe Constants of Motion}, journal = {Communications in Computational Physics}, year = {2013}, volume = {14}, number = {4}, pages = {1094--1102}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.181212.220113a}, url = {http://global-sci.org/intro/article_detail/cicp/7194.html} }
TY - JOUR T1 - A Constructive Method for Computing Generalized Manley-Rowe Constants of Motion AU - Elena Kartashova & Loredana Tec JO - Communications in Computational Physics VL - 4 SP - 1094 EP - 1102 PY - 2013 DA - 2013/10 SN - 14 DO - http://doi.org/10.4208/cicp.181212.220113a UR - https://global-sci.org/intro/article_detail/cicp/7194.html KW - AB -

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.

Elena Kartashova and Loredana Tec. (2013). A Constructive Method for Computing Generalized Manley-Rowe Constants of Motion. Communications in Computational Physics. 14 (4). 1094-1102. doi:10.4208/cicp.181212.220113a
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