Peaked wave solutions of Camassa-Holm equation

Chaos, Solitons and Fractals

Volumn 19, Issue 1, 2004, Pages 77-92

  Liu, Zheng Rong ^a,b   Wang, Rui Qi ^b   Jing, Zhu Jun ^b,c  

^a YUNNAN UNIVERSITY   (China)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^c HUNAN NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; SOLITONS; WAVE EQUATIONS;

WAVE SOLUTIONS;

WATER WAVES;

EID: 0038111998     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(03)00082-1     Document Type: Article

References (20)

1. Camassa R., Holm D.D. An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71(11):1993;1661-1664.
2. Boyd J.P. Peakons and coshoidal waves: travelling wave solutions of the Camassa-Holm equation. Appl. Math. Comput. 81(2-3):1997;173-187.
3. Qian T., Tang M. Peakons and periodic cusp waves in a generalized Camassa-Holm equation. Chaos, Solitons & Fractals. 12:2001;1347-1360.
4. Liu Z., Qian T. Peakons of the Camassa-Holm equation. Appl. Math. Model. 26:2002;473-480.
5. Cooper F., Shepard H. Solitons in the Camassa-Holm shallow water equation. Phys. Let.t A. 194(4):1994;246-250.
6. Fuchssteiner B. Some tricks from the symmetry-toolbox for nonlinear equations: generalizations of the Camassa-Holm equation. Phys. D. 95(3-4):1996;229-243.
7. Constantin A. On the Cauchy problem for the periodic Camassa-Holm equation. J. Differen. Equat. 141(2):1997;218-235.
8. Constantin A. Quasi-periodicity with respect to time of spatially periodic finite-gap solution of the Camassa-Holm equation. Bull. Sci. Math. 127(7):1998;487-494.
9. Dai H.H., Pavlov M. Maxim transformations for the Camassa-Holm equation, its high-frequency limit and the sinh-gordon equation. J. Phys. Soc. Jpn. 67(11):1998;3655-3657.
10. Schiff J. The Camassa-Holm equation: a loop group approach. Phys. D. 121(1-2):1998;24-43.
11. Kouranbaeva S. The Camassa-Holm equation as a geodesic flow on the diffeomorphism group. J. Math. Phys. 40(2):1999;857-868.
12. Liu Z., Qian T. Peakons and their bifurcation in a generalized Camassa-Holm equation. Int. J. Bifurcat. Chaos. 11(3):2001;781-792.
13. Alber M.S., Camassa R., Fedorov Y.N., Holm D.D., Marshen J.E. The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDE's of shallow water and Dym type. Comm. Math. Phys. 221(1):2001;197-227.
14. Constantin A., Strauss W.A. Stability of the Camassa-Holm solitons. J. Nonlinear Sci. 12:2002;415-422.
15. Reyes E.G. Geometric integrability of the Camassa-Holm equation. Lett. Math. Phys. 59(2):2002;117-131.
16. Foias C., Holm D.D., Titi E.S. The three dimenional viscous Camassa-Holm equation, and their relation to the Navier-Stokes equations and turbulence theory. J. Dynam. Differen. Equat. 14(1):2002;1-35.
17. Lenells J. The scattering approach for the Camassa-Holm equation. J. Nonlinear Math. Phys. 9(4):2002;389-393.
18. Johnson R.S. Camassa-Holm, Korteweg-de Vries and related models for water waves. J. Fluid. Mech. 455:2002;63-82.
19. Guckenheimer J., Holmes P. Dynamical systems and bifurcation of vector fields. 1983;Springer, New York.
20. Wiggins S. Introduction to applied nonlinear dynamical systems and chaos. 1990;Springer-Verlag, New York.