The multiple-soliton solution of the Camassa-Holm equation

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 460, Issue 2049, 2004, Pages 2617-2627

  Li, Yishen ^a   Zhang, Jin E ^b,c  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Camassa Holm equation; Darboux transformation; Solitons

Indexed keywords

ALGORITHM; ARTICLE; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL;

EID: 17144394784     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2004.1331     Document Type: Article

References (17)

1. Busuioc, V. 1999 On second grade fluid with vanishing viscosity. C. R. Acad. Sci. Paris Sér. I 328, 1241-1246.
2. Camassa, R. & Holm, D. D. 1993 An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71(11), 1661-1664.
3. Camassa, R., Holm, D. D. & Hyman, J. 1994 A new integrable shallow water equation. Adv. Appl. Mech. 31, 1-33.
4. Constantin, A. 2001 On the scattering problem for the Camassa-Holm equation. Proc. R. Soc. Lond. A 457, 953-970.
5. Constantin, A. & Lenells, J. 2003 On the inverse scattering approach for an integrable shallow water wave equation. Phys. Lett. A 308, 432-436.
6. Dai, H.-H. 1998 Model equations for nonlinear dispersive waves in compressible Mooney-Rivlin rod. Acta Mech. 127, 193-207.
7. Dullin, H. R., Gottwald, G. A. & Holm, D. D. 2001 An integrable shallow water equation with linear and nonlinear dispersion. Phys. Rev. Lett. 87, 194501.
8. Fokas, A. S. & Liu, Q. M. 1996 Asymptotic integrability of water waves. Phys. Rev. Lett. 77, 2347-2351.
9. Fuchssteiner, B. & Fokas, A. 1981 Symplectic structures, their Bäcklund transformation and hereditary symmetries. Physica D 4, 47-66.
10. Johnson, R. S. 2002 Camassa-Holm, Korteweg-de Vries and related models for water waves. J. Fluid Mech. 455, 63-82.
11. Johnson, R. S. 2003 On solutions of the Camassa-Holm equation. Proc. R. Soc. Lond. A 459, 1687-1708.
12. Li, Y.-S. & He, J.-S. 1998 Exact solution of the Schrödinger equation for the time-dependent harmonic oscillator. Chin. Sci. Bull. 43, 1066-1071.
13. McKean, H. P. 2003 The Liouville correspondence between the Korteweg-de Vries and the Camassa-Holm hierarchies. Commun. Pure Appl. Math. 56, 998-1015.
14. Matveev, V. B. & Salle, M. A. 1991 Darboux transformations and solitons. Springer.
15. Misiolek, G. 1998 A shallow water equation as a geodesic flow on the Bott-Virasoro group. J. Geom. Phys. 24, 203-208.
16. -3 = 0. Proc. Am. Math. Soc. 1, 681.
17. Schiff, J. 1998 The Camassa-Holm equation: a loop group approach. Physica D 121, 24-43.