Euler-Poincaré formalism of KDV-burgers and higher order nonlinear Schrödinger equations

Regular and Chaotic Dynamics

Volumn 7, Issue 4, 2002, Pages 425-434

  Guha, P ^a,b  

^a UNIVERSITY OF MISSOURI   (United States)

^b S N BOSE NATIONAL CENTRE FOR BASIC SCIENCES   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 35748938605     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1070/RD2002v007n04ABEH000220     Document Type: Article

References (28)

1. V. I. Arnold. Sur la géométrie differentielle des groupes de Lie de dimension infinite et ses applications á l'hydrodynamique des fluids parfaits. Ann. Inst. Fouries, Grenoble. V. 16. 1966. P. 319-361.
2. V. I. Arnold. Mathematical methods of classical mechanics, second edition, Graduate Texts in Mathematics. V. 60. Springer-Verlag. 1989.
3. R. Camassa, D. D. Holm. An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. V. 71. 1993. P. 1661-1664.
4. D. Ebin, J. E. Marsden. Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. Math., V. 92. 1970. P. 102-163.
5. 1 and Integrable systems. To appear in Jour. Geom. Phys.
6. 1) and Adler-Gelfand-Dikii spaces and integrable systems. Letters in Mathematical Physics. V. 55, i. 2001. P. 17-31.
7. 1, projective structures and integrable systems, to appear in Kruskal 2000 conference proceedings. Also the longer version is available (IHES/M/00/24); http://www.ihes.fr/information/ preprintM00.html.
8. P. Guha. Projective connections, AGD manifold and integrable systems. Kev. Math. Phys. V. 12. No10. 2000. P. 1391-1406.
9. A. Hasegawa, F. P. Tappert. Appl. Phys. Lett. V. 23. 1973. P. 142.
10. A. A. Kirillov. Infinite dimensional Lie groups: their orbits, invariants and representations. The geometry of moments. Lect. Notes in Math. Springer-Verlag. V. 970. 1982. P. 101-123.
11. A. Kirillov. The orbit method, I and II : Infinite-dimensional Lie groups and Lie algebras. Contemporary Mathematics. V. 145. 1993.
12. B. A. Kupershmidt. Dark Equations. J. Nonlinear Math. Phys. V. 8. No3. 2001. P. 363-445.
13. V. F. Lazutkin, T. F. Pankratova. Normal forms and the versal deformations for Hill's equation. Funct. Anal. Appl. V. 9(4). 1975. P. 41-48.
14. S.-D. Liu. S.-U.Liu. Sincia Sinica, A9, 938. 1991. (In Chinese)
15. M. A. Malkov. Spatial chaos in weakly dispersive and nonviscous media: a nonperturbative theory of the driven KdV-Burgers equation, chaos-dyn/9603013.
16. B. A. Malomed, B.-F. Feng, T. Kawahara. A stabilized Kuramoto-Sivashinsky system. nlin.PS/0108004.
17. P. Marcel, V. Ovsienko, C. Roger. Extension of the Virasoro and Neveu-Schwartz algebras and generalized Sturm-Liouville operators. Lett. Math. Phys. V. 40. P. 31-39. 1997
18. J. E. Marsden, T. S. Ratiu. Introduction to Mechanics and Symmetry. Texts in Applied Mathematics 17. 1994, Second Edition (1999). Springer-Verlag.
19. G. Misiolek. A shallow water equation as a geodesic How on the Bott-Virasoro group. J. Geom. Phys. V. 24. 1998. P. 203-208.
20. L. F. Mollenauer, R. H. Stolen. J. P. Gordon. Phys. Rev. Lett. V. 45. 1980. P. 1095.
21. Y. Nakamura, H. Bailung, P. K. Shukla. Observation of Ion-Acoustic shocks in a dusty plasma. Phys. Rev. Letts. V. 83. 1999. P. 8031-9007.
22. V. Ovsienko, B. Khesin. KdV super equation as an Euler equation. Funt. Anal. Appl. V. 21. 1987. P. 329-331.
23. 1. Fund. Anal. Appl. V. 30. No4. 1996. P. 290-291.
24. G. Segal. Unitary representations of some infinite dimensional groups. Comm. Math. Phys. V. 80. 1981. P. 301-342.
25. 1 metric and mean hydrodynamics. J. Funct. Anal. V. 160. 1998. P. 337-365.
26. G. Wilson. On the quasi-Hamiltonian formalism of the KdV equation. Phys. Lett. A. V. 132. No3. 1988. P. 445-450.
27. G. Wilson. On antiplectic pairs in the Hamiltonian formalism of evolution equations. Quart. J. Math. V. 42. 1991. P. 227-256.
28. E. Witten. Coadjoint orbits of the Virasoro group. Comm. Math. Phys. V. 114. 1988. P. 1-53.