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Volume 6, Issue 1
Generating Function Methods for Coefficient-Varying Generalized Hamiltonian Systems

Xueyang Li, Aiguo Xiao & Dongling Wang

DOI: 10.4208/aamm.12-m12112

Adv. Appl. Math. Mech., 6 (2014), pp. 87-106.

Published online: 2014-06

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  • 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).

  • Keywords

Generalized Hamiltonian systems, Poisson manifolds, generating functions, structure-preserving algorithms, generalized Lotka-Volterra systems.

  • AMS Subject Headings

65P10, 65L05, 37M15, 70H05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-6-87, author = {Li , XueyangXiao , Aiguo and Wang , Dongling}, title = {Generating Function Methods for Coefficient-Varying Generalized Hamiltonian Systems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {1}, pages = {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).

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-m12112}, url = {http://global-sci.org/intro/article_detail/aamm/6.html} }
TY - JOUR T1 - Generating Function Methods for Coefficient-Varying Generalized Hamiltonian Systems AU - Li , Xueyang AU - Xiao , Aiguo AU - Wang , Dongling JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 87 EP - 106 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.12-m12112 UR - https://global-sci.org/intro/article_detail/aamm/6.html KW - Generalized Hamiltonian systems, Poisson manifolds, generating functions, structure-preserving algorithms, generalized Lotka-Volterra systems. AB -

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).

Li , XueyangXiao , Aiguo and Wang , Dongling. (2014). Generating Function Methods for Coefficient-Varying Generalized Hamiltonian Systems. Advances in Applied Mathematics and Mechanics. 6 (1). 87-106. doi:10.4208/aamm.12-m12112
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