Difference discrete variational principles, Euler-Lagrange cohomology and symplectic, multisymplectic structures I: Difference discrete variational principle

Communications in Theoretical Physics

Volumn 37, Issue 1, 2002, Pages 1-10

  Guo, Han Ying ^a   Li, Yu Qi ^a   Wu, Ke ^a,b   Wang, Shi Kun ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b CAPITAL NORMAL UNIVERSITY   (China)

Author keywords

Discrete variation; Euler Lagrange cohomology; Symplectic structure

Indexed keywords

EID: 0036004106     PISSN: 02536102     EISSN: None     Source Type: Journal    
DOI: 10.1088/0253-6102/37/1/1     Document Type: Article

References (23)

1. V.I. Arnold, Mathematical Methods of Classical Mechanics, Graduate Texts in Math. 60 (1978), second ed., Springer-Verlag (1989).
2. R. Abraham and J.E. Marsden, Foundation of Mechanics, second ed., Addison-Wesley (1978).
3. E. Binz, J. Śniatycki and H. Ficher, Geometry of Classical Fields, North Holland Elsevier, Amsterdam (1988).
4. T.J. Bridges, Math. Proc. Camb. Phil. Soc. 121 (1997) 147.
5. M. Gotay, J. Isenberg and J.E. Marsden, "Momentum Maps and the Hamiltonian Structure of Classical Relativistic Field Theories", (1997) preprint.
6. J.E. Marsden and S. Shkoller, Math. Proc. Camb. Phil. Soc. 125 (1999) 535.
7. J.E. Marsden, G.W. Patrick and S. Shkoller, Comm. Math. Phys. 199 (1998) 351.
8. R.D. Ruth, IEEE Trans. Nucl. Sci. 30 (1983) 1669.
9. K. Feng, "On Difference Schemes and Symplectic Geometry", Proc. 1984 Beijing Symposium on Differential Geometry and Differential Equations - Computation of Partial Differential Equations, ed. FENG Kang, Science Press, Beijing (1985); Selected Works of FENG Kang II (1995), and the references therein.
10. K. Feng, "On Difference Schemes and Symplectic Geometry", Proc. 1984 Beijing Symposium on Differential Geometry and Differential Equations - Computation of Partial Differential Equations, ed. FENG Kang, Science Press, Beijing (1985); Selected Works of FENG Kang II (1995), and the references therein.
11. J.M. Sanz-Serna and M.P. Calvo, Numerical Hamiltonian Problems, Chapman and Hall, London (1994), and the references therein.
12. H.Y. GUO, Y.Q. LI and K. WU, Commun. Theor. Phys. (Beijing, China) 35 (2001) 703.
13. H.Y. GUO, "Symplectic, Multisymplectic Structures and the Euler-Lagrange Cohomology", talk given at The International Workshop on Structure-Preserving Algorithms, March 25-31, Beijing (2001).
14. H.Y. GUO, Y.Q. LI and K. WU, Commun. Theor. Phys. (Beijing, China) 36 (2001) 11.
15. H.Y. GUO, X.M. JI, Y.Q. LI and K. WU, Commun. Theor. Phys. (Beijing, China) 36 (2001) 259.
16. K. WU, "Symplectic and Multisymplectic 2-Form Structures in Simple Finite Element Method", talk given at The International Workshop on Structure-Preserving Algorithms, March 25-31, Beijing (2001).
17. H.Y. GUO, X.M. JI, Y.Q. LI and K. WU, preprint AS-ITP-2001-010, April, hep-th/0104151 (2001).
18. H.Y. GUO, Y.Q. LI, K. WU and S.K. WANG, preprint AS-ITP-2001-009, April, hep-th/0104140 (2001).
19. H.Y. GUO, K. WU, S.H. WANG, S.K. WANG and G.M. WEI, Commun. Theor. Phys. (Beijing, China) 34 (2000) 307.
20. H.Y. GUO, K. WU and W. ZHANG, Commun. Theor. Phys. (Beijing, China) 34 (2000) 245.
21. R. Courant and D. Hilbert, Methods of Mathematical Physics, Interscience, New York (1953).
22. A.P. Veselov, Funkts. Anal. Prilozhen 22 (1988) 1.
23. J. Moser and A.P. Veselov, Comm. Math. Phys. 139 (1991) 217.