On Symplectic and Multisymplectic Structures and Their Discrete Versions in Lagrangian Formalism

Communications in Theoretical Physics

Volumn 35, Issue 6, 2001, Pages 703-710

  Guo, Han Ying ^a   Li, Yu Qi ^a   Wu, Ke ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

Difference discrete variational principle; Euler lagrange cohomology; Symplectic structure

Indexed keywords

EID: 0035617778     PISSN: 02536102     EISSN: None     Source Type: Journal    
DOI: 10.1088/0253-6102/35/6/703     Document Type: Article

References (18)

1. K. Feng, "On Difference Schemes and Symplectic Geometry," Proc. of the 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.
2. K. Feng, "On Difference Schemes and Symplectic Geometry," Proc. of the 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.
3. J.M. Sanz-Serna and M.P. Calvo, Numerical Hamiltonian Problems, Chapman and Hall, London (1994), and the references therein.
4. T.J. Bridges, Math. Proc. Camb. Phil. Soc. 121 (1997) 147.
5. J.E. Marsden, G.W. Patrick and S. Shkoller, Commun. Math. Phys. 199 (1998) 351, and the references therein.
6. H.Y. GUO, K. WU, S.H. WANG, S.K. WANG and G.M. WEI, Commun. Theor. Phys. (Beijing, China) 34 (2000) 307.
7. H.Y. GUO, K. WU and W. ZHANG, Commun. Theor. Phys. (Beijing, China) 34 (2000) 245.
8. H.Y. GUO, Talk given at the Workshop on Quantum Field Theories, Dec. 14-19 (1998), Zhongshan University, Guangzhou; H.Y. GUO, K. WU, S.H. WANG and G.M. WEI, "Discrete Symplectic Algorithm on Regular Lattice", Talk given by H.Y. GUO at the CCAST-WL Workshop on Computational Methods and Their Applications in Physics and Mechanics, March (1999); the CCAST-WL Workshop on Genetic Algorithm and Its Applications, April (1999); the CCAST-WL Workshop on Integrable System, May 3-7 (1999); CCAST-WL Workshop Series 104, pp 167-192; H.Y. GUO, "Noncommutative Differential Calculus and Discrete Symplectic Algorithm on Regular Lattice", Talk given at the CCAST-WL Workshop on Structure Preserving Algorithms and Applications, Dec. 13-17 (1999); CCAST-WL Workshop Series 118, pp 1-16.
9. H.Y. GUO, Talk given at the Workshop on Quantum Field Theories, Dec. 14-19 (1998), Zhongshan University, Guangzhou; H.Y. GUO, K. WU, S.H. WANG and G.M. WEI, "Discrete Symplectic Algorithm on Regular Lattice", Talk given by H.Y. GUO at the CCAST-WL Workshop on Computational Methods and Their Applications in Physics and Mechanics, March (1999); the CCAST-WL Workshop on Genetic Algorithm and Its Applications, April (1999); the CCAST-WL Workshop on Integrable System, May 3-7 (1999); CCAST-WL Workshop Series 104, pp 167-192; H.Y. GUO, "Noncommutative Differential Calculus and Discrete Symplectic Algorithm on Regular Lattice", Talk given at the CCAST-WL Workshop on Structure Preserving Algorithms and Applications, Dec. 13-17 (1999); CCAST-WL Workshop Series 118, pp 1-16.
10. H.Y. GUO, Talk given at the Workshop on Quantum Field Theories, Dec. 14-19 (1998), Zhongshan University, Guangzhou; H.Y. GUO, K. WU, S.H. WANG and G.M. WEI, "Discrete Symplectic Algorithm on Regular Lattice", Talk given by H.Y. GUO at the CCAST-WL Workshop on Computational Methods and Their Applications in Physics and Mechanics, March (1999); the CCAST-WL Workshop on Genetic Algorithm and Its Applications, April (1999); the CCAST-WL Workshop on Integrable System, May 3-7 (1999); CCAST-WL Workshop Series 104, pp 167-192; H.Y. GUO, "Noncommutative Differential Calculus and Discrete Symplectic Algorithm on Regular Lattice", Talk given at the CCAST-WL Workshop on Structure Preserving Algorithms and Applications, Dec. 13-17 (1999); CCAST-WL Workshop Series 118, pp 1-16.
11. H.Y. GUO, Talk given at the Workshop on Quantum Field Theories, Dec. 14-19 (1998), Zhongshan University, Guangzhou; H.Y. GUO, K. WU, S.H. WANG and G.M. WEI, "Discrete Symplectic Algorithm on Regular Lattice", Talk given by H.Y. GUO at the CCAST-WL Workshop on Computational Methods and Their Applications in Physics and Mechanics, March (1999); the CCAST-WL Workshop on Genetic Algorithm and Its Applications, April (1999); the CCAST-WL Workshop on Integrable System, May 3-7 (1999); CCAST-WL Workshop Series 104, pp 167-192; H.Y. GUO, "Noncommutative Differential Calculus and Discrete Symplectic Algorithm on Regular Lattice", Talk given at the CCAST-WL Workshop on Structure Preserving Algorithms and Applications, Dec. 13-17 (1999); CCAST-WL Workshop Series 118, pp 1-16.
12. H.Y. GUO, Talk given at the Workshop on Quantum Field Theories, Dec. 14-19 (1998), Zhongshan University, Guangzhou; H.Y. GUO, K. WU, S.H. WANG and G.M. WEI, "Discrete Symplectic Algorithm on Regular Lattice", Talk given by H.Y. GUO at the CCAST-WL Workshop on Computational Methods and Their Applications in Physics and Mechanics, March (1999); the CCAST-WL Workshop on Genetic Algorithm and Its Applications, April (1999); the CCAST-WL Workshop on Integrable System, May 3-7 (1999); CCAST-WL Workshop Series 104, pp 167-192; H.Y. GUO, "Noncommutative Differential Calculus and Discrete Symplectic Algorithm on Regular Lattice", Talk given at the CCAST-WL Workshop on Structure Preserving Algorithms and Applications, Dec. 13-17 (1999); CCAST-WL Workshop Series 118, pp 1-16.
13. H.Y. GUO, Talk given at the Workshop on Quantum Field Theories, Dec. 14-19 (1998), Zhongshan University, Guangzhou; H.Y. GUO, K. WU, S.H. WANG and G.M. WEI, "Discrete Symplectic Algorithm on Regular Lattice", Talk given by H.Y. GUO at the CCAST-WL Workshop on Computational Methods and Their Applications in Physics and Mechanics, March (1999); the CCAST-WL Workshop on Genetic Algorithm and Its Applications, April (1999); the CCAST-WL Workshop on Integrable System, May 3-7 (1999); CCAST-WL Workshop Series 104, pp 167-192; H.Y. GUO, "Noncommutative Differential Calculus and Discrete Symplectic Algorithm on Regular Lattice", Talk given at the CCAST-WL Workshop on Structure Preserving Algorithms and Applications, Dec. 13-17 (1999); CCAST-WL Workshop Series 118, pp 1-16.
14. H.Y. GUO, Talk given at the Workshop on Quantum Field Theories, Dec. 14-19 (1998), Zhongshan University, Guangzhou; H.Y. GUO, K. WU, S.H. WANG and G.M. WEI, "Discrete Symplectic Algorithm on Regular Lattice", Talk given by H.Y. GUO at the CCAST-WL Workshop on Computational Methods and Their Applications in Physics and Mechanics, March (1999); the CCAST-WL Workshop on Genetic Algorithm and Its Applications, April (1999); the CCAST-WL Workshop on Integrable System, May 3-7 (1999); CCAST-WL Workshop Series 104, pp 167-192; H.Y. GUO, "Noncommutative Differential Calculus and Discrete Symplectic Algorithm on Regular Lattice", Talk given at the CCAST-WL Workshop on Structure Preserving Algorithms and Applications, Dec. 13-17 (1999); CCAST-WL Workshop Series 118, pp 1-16.
15. H.Y. GUO, Y.Q. LI and K. WU, "Symplectic, Multisymplectic Structures and Euler-Lagrange Cohomology", in preparation.
16. A.P. Veselov, Funkts. Anal. Prilozhen 22 (1988) 1.
17. J. Moser and A.P. Veselov, Commun. Math. Phys. 139 (1991) 217.
18. S. Reich, J. Comput. Phys. 157 (2000) 473.