A shallow water equation as a geodesic flow on the Bott - Virasoro group

Journal of Geometry and Physics

Volumn 24, Issue 3, 1998, Pages 203-208

  Misiołek, Gerard ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

Bott Virasoro group; Shallow water equations

Indexed keywords

EID: 0031989845     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(97)00010-7     Document Type: Article

References (11)

1. [A] V.I. Arnol'd, Mathematical Methods of Classical Mechanics, 2nd Ed. (Springer, Berlin, 1989).
2. [B] R. Bott, On the characteristic classes of groups of diffeomorphisms, Enseign, Math. 23 (1977).
3. [CH] R. Camassa and D. Holm, An integrable shallow water equation with peaked solutions, Phys. Rev. Lett. 71 (1993).
4. [CHH] R. Camassa, D. Holm and J. Hyman, A new integrable shallow water equation, Adv. Appl. Mech. 31 (1994).
5. [CE] J. Cheeger and D.G. Ebin, Comparison Theorems in Riemannian Geometry (North-Holland, New York, 1975).
6. [GF] I.M. Gelfand and D.B. Fuchs, The cohomology of the Lie algebra of vector fields on a circle, Funktsional Anal. Prilozhen. 2 (1968).
7. [MR] J. Marsden and T. Ratiu, Introduction to Mechanics and Symmetry (Springer, Berlin, 1995).
8. [M1] G. Misiołek, Stability of flows of ideal fluids and the geometry of the group of diffeomorphisms. Indiana Univ. Math. J. 42 (1993).
9. [M2] G. Misiołek, Conjugate points in the Bott - Virasoro group and the KdV equation, Proc. AMS, to appear.
10. [OK] V. Ovsienko and B. Khesin, Korteweg - de Vries superequations as an Euler equation, Functional Anal. Appl. 21 (1987).
11. [PS] A. Pressley and G. Segal, Loop Groups (Oxford University Press, Oxford, 1986).