收稿日期: 2002-04-10
修回日期: 2002-06-17
网络出版日期: 2003-03-10
Multisymplectic Geometrical Approach for the Variational PDEs Connected with the Characteristics of the Vector Fields
Received date: 2002-04-10
Revised date: 2002-06-17
Online published: 2003-03-10
Supported by
supported by the National Nature Science Foundation of China (49975008)and by the Special Funds for Major State Basic Research Projects (G 1999,032800)
赵平福 , 秦孟兆 . 联系向量场特征的变分方程多辛几何方法(英文)[J]. 中国科学院大学学报, 2003 , 20(2) : 160 -167 . DOI: 10.7523/j.issn.2095-6134.2003.2.005
Connecting the characteristics of the vector fields we consider the multisymplectic geometrical approach for the variational PDEs. We analyze the conservation laws induced by the multisymplectic form formula and give the characteristics of these conservation laws when variational symmetries are taken into account.
[1] J E Marsden, G P Patrick, S Shkoller. Multisymplectic geometry, variational integrators, and Nonlinear PDEs. Comm Math Phys,1998, 199: 351~395
[2] J E Marsden, S Shkoller. Multisymplectic Geometry, Covariant Hamiltonians, and Water Waves. Math Proc Camb Phil Soc, 1999, 125
[3] P F Zhao, M Z Qin. Multisymplectic Geometry and Multisymplectic Preissmann Scheme for the KdV Equation. J Phys A: Math Gen, 2000, 33: 3613~3626
[4] Shinar Kouranbaeva, Steve Shkoller. A Variational Approach to Second-Order Multisymplectic Field Theory. Department of mathematics, university of California, Santa Cruz, CA 95064, preprint
[5] P J Olver. Applications of Lie Groups to Differential Equations. New York: Springer-Verlag, 1986
[6] M J Gotay. A Multisymplectic Approach to the KdV Equation, published in: Differential Geometrical Methods in Theoretical Physics. In: K Bleuler, M Werner, Eds. NATO Advanced Science Institute Series C: Mathematical and Physical Sciences. Vol. 250, 295~305
[7] M J Gotay. A Multisymplectic Framework for Classical Field Theory and the Calculus of Variations I: Covariant Hamiltonian Formulation, Mechanics, Analysis and Geometry: 200 Years After Lagrange. M Francaviglia, Ed. (North Holland), 203~235
[8] George W Bluman, Sukeyuki Kumei. Symmetries and Differential Equations, Applied Mathematics Sciences. Springer-Verlag, 1991
/
| 〈 |
|
〉 |