Year: 2014
Author: Xueyang Li, Aiguo Xiao, Dongling Wang
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 1 : pp. 87–106
Abstract
The generating function methods have been applied successfully to generalized Hamiltonian systems with constant or invertible Poisson-structure matrices. In this paper, we extend these results and present the generating function methods preserving the Poisson structures for generalized Hamiltonian systems with general variable Poisson-structure matrices. In particular, some obtained Poisson schemes are applied efficiently to some dynamical systems which can be written into generalized Hamiltonian systems (such as generalized Lotka-Volterra systems, Robbins equations and so on).
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.12-m12112
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 1 : pp. 87–106
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Generalized Hamiltonian systems Poisson manifolds generating functions structure-preserving algorithms generalized Lotka-Volterra systems.