The Camassa - Holm equation as a geodesic flow on the diffeomorphism group

Journal of Mathematical Physics

Volumn 40, Issue 2, 1999, Pages 857-868

  Kouranbaeva, Shinar ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033483085     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532690     Document Type: Article

References (16)

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6. 1 metric and mean hydrodynamics," J. Funct. Anal. 160, 337-365 (1998).
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9. M. Spivak, Differential Geometry (Brandeis University, Waltham, MA, 1970), Vols. 1-5.
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11. V. Arnold, "Sur la géometrie différentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits," Ann. Inst. Fourier Grenoble 16, 319-361 (1966).
12. D. Bao and T. Ratiu, "On a Monge - Ampére equation and some geometry of diffeomorphism groups" (unpublished).
13. V. Arnold, Mathematical Methods of Classical Mechanics (Springer, New York, 1978).
14. J. E. Marsden, D. Ebin, and A. Fischer, "Diffeomorphism groups, hydrodynamics and relativity," in Proceedings of the 13th Biennial Seminar of the Canadian Mathematical Congress on Differential Topology: Differential Geometry and Applications (Vanstone, Montreal, 1972), pp. 135-279.
15. G. Misiolek, "A shallow water equation as a geodesic flow on the Bott - Virasoro group," J. Geom. Phys. 24, 203-208 (1998).
16. M. Alber, R. Camassa, D. D. Holm, and J. E. Marsden, "The geometry of peaked solitons and billiard solutions of a class of integrable pde's," Lett. Math. Phys. 32, 137-151 (1994).