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 - <p style="text-align: justify;">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).</p>