Abstract
The nature of infinite-dimensional Hamiltonian systems are studied for the purpose of further study on some generalized Hamiltonian systems equipped with a given Poisson bracket. From both theoretical and practical viewpoints, we summarize a general method of constructing symplectic-like difference schemes of these kinds of systems. This study provides a new algorithm for the application of the symplectic geometry method in numerical solutions of general evolution equations.
| Original language | English |
|---|---|
| Pages (from-to) | 719-725 |
| Number of pages | 7 |
| Journal | Advances in Atmospheric Sciences |
| Volume | 19 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2002 |
Funding
GMbal potential vorticity (sI ) -0.000000000 000 000 02 -0.000 000 000 000 000 O0 --0.000 000 000 000 000 08 -0.000 000 000 000 000 04 0.000 000 000000 000 13 --0.000 000 000 000 000 10 0.000 000 000 000 000 02 0.00000000000000022 Acknowledgments. This work was supported by the China National Key Development Planning Project for Basic Research (Abbreviation: 973 Project; Grant No. G1999032801), the Chinese Academy of Sciences Key Innovation Direction Project (Grant No. KZCX2208) and the National Natural Science Foundation of China (Grant No. 49975020), and the National Outstanding Youth Scientist Foundation of China (Grant No. 49825109).
Keywords
- Generalized Hamiltonian systems
- Infinite-dimensional Hamiltonian systems
- Poisson brackets
- Symplectic-like difference schemes