The supersymmetric Camassa-Holm equation and geodesic flow on the superconformal group

Journal of Mathematical Physics

Volumn 42, Issue 1, 2001, Pages 260-273

  Devchand, Chandrashekar ^a,b   Schiff, Jeremy ^c  

^a MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

^b MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^c BAR ILAN UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035581753     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1330196     Document Type: Article

References (26)

1. R. Camassa and D. D. Holm, "An integrable shallow water equation with peaked solitons," Phys. Rev. Lett. 71, 1661 (1993).
2. R. Camassa, D. D. Holm, and J. M. Hyman, "A new integrable shallow water equation with peaked solutions," in Advances in Applied Mechanics, edited by J. Hutchinson and T. Wu (Academic, New York, 1994), Vol. 31, pp. 1-33.
3. A. Fokas and B. Fuchssteiner, "Symplectic structures, their Bäcklund transformations and hereditary symmetries," Physica D 4, 47-66 (1981).
4. V. I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, 1978).
5. V. Yu. Ovsienko and B. A. Khesin, "Korteweg-de Vries superequation as an Euler equation," Funct. Anal. Appl. 21, 329-331 (1987).
6. G. Misiolek, "Conjugate points in the Bott-Virasoro group and the KdV equation," Proc. Am. Math. Soc. 125, 935-940 (1997).
7. V. I. Arnold and B. A. Khesin, Topological Methods in Hydrodynamics (Springer-Verlag, New York, 1998).
8. P. W. Michor and T. S. Ratiu, "On the geometry of the Virasoro-Bott group," J. Lie Theory 8, 293-309 (1998).
9. G. Misiolek, "A shallow water equation as a geodesic flow on the Bott-Virasoro group," J. Geom. Phys. 24, 203-208 (1998).
10. 1 metric and mean hydrodynamics," J. Funct. Anal. 160, 337-365 (1998).
11. S. Kouranbaeva, "The Camassa-Holm equation as a geodesic flow on the diffeomorphism group," J. Math. Phys. 40, 857-868 (1999).
12. O. B. Fringer and D. D. Holm, "Integrable vs nonintegrable geodesic soliton behavior," solv-int/9903007.
13. B. A. Kupershmidt, "A super Korteweg-de Vries equation: an integrable system," Phys. Lett. A 102, 213-215 (1984).
14. P. Mathieu, "Supersymmetric extension of the Korteweg-de Vries equation," J. Math. Phys. 29, 2499-2506 (1988).
15. Yu. I. Manin and A. O. Radul, "A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy," Commun. Math. Phys. 98, 65-77 (1988).
16. D. Zhang, "Integrability of fermionic extensions of the Korteweg-de Vries equation," Phys. Lett. A 234, 358-360 (1997).
17. N. S. Manton, "Deconstructing supersymmetry," J. Math. Phys. 40, 736-750 (1999).
18. C. Devchand and J. Schiff, "Deconstructing super-KdV," in preparation.
19. J. Schiff, "The Camassa-Holm equation: A loop group approach," Physica D 121, 24-43 (1998).
20. J. Weiss, M. Tabor, and G. Carnevale, "The Painlevé property for partial differential equations," J. Math. Phys. 24, 522-526 (1983).
21. A. N. W. Hone, "The associated Camassa-Holm equation and the KdV equation," J. Phys. A 32, L307-L314 (1999).
22. A. Ramani, B. Grammaticos, and T. Bountis, "The Painlevé property and singularity analysis of integrable and non-integrable systems," Phys. Rep. 180, 159-245 (1989).
23. F. Calogero, "An integrable Hamiltonian system," Phys. Lett. A 201, 306-310 (1995); F. Calogero, "A solvable Hamiltonian system," J. Math. Phys. 36, 4832-4840 (1995); F. Calogero and J. P. Francoise, "A completely integrable Hamiltonian system," ibid. 37, 2863-2871 (1996);
24. F. Calogero, "An integrable Hamiltonian system," Phys. Lett. A 201, 306-310 (1995); F. Calogero, "A solvable Hamiltonian system," J. Math. Phys. 36, 4832-4840 (1995); F. Calogero and J. P. Francoise, "A completely integrable Hamiltonian system," ibid. 37, 2863-2871 (1996);
25. F. Calogero, "An integrable Hamiltonian system," Phys. Lett. A 201, 306-310 (1995); F. Calogero, "A solvable Hamiltonian system," J. Math. Phys. 36, 4832-4840 (1995); F. Calogero and J. P. Francoise, "A completely integrable Hamiltonian system," ibid. 37, 2863-2871 (1996);
26. O. Ragnisco and M. Bruschi, "Peakons, R-Matrix and Toda lattice," Physica A 228, 150-159 (1996).