New peaked solitary wave solutions of the generalized Camassa-Holm equation

Chaos, Solitons and Fractals

Volumn 19, Issue 3, 2004, Pages 621-637

  Tian, Lixin ^a   Song, Xiuying ^a  

^a JIANGSU UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); HAMILTONIANS; NAVIER STOKES EQUATIONS; NONLINEAR EQUATIONS; REYNOLDS NUMBER; WAVE EQUATIONS;

TRAVELING WAVES;

SOLITONS;

EID: 0043132083     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(03)00192-9     Document Type: Article

References (18)

1. Camassa R., Holm D. An integrable shallow water equation with peaked soliton. Phys. Rev. Lett. 71:1993;1661-1664.
2. Fisher M., Sshiff J. The Camassa-Holm equation: conserved quantities and the initial value problem. Phys. Lett. A. 259(3):1999;371-376.
3. Clarkson D.A., Mansfiel E.L., Priestley T.J. Symmetries of a class of nonlinear third-order partial differential equations. Math. Comput. Modell. 25(819):1997;195-212.
4. Kraenkel R.A., Senthilvelsn M., Zenchuk A.I. On the integrable perturbations of the Camassa-Holm equation. J. Math. Phys. 41(5):2000;3160-3169.
5. Cooper F., Shepard H. Solitons in the Camassa-Holm shallow water equation. Phy. Lett. A. 194:1994;246-250.
6. Tian L., Xu G., Liu Z. The concave or convex peaked and smooth solutions of Camassa-Holm equation. Appl. Math. Mech. 23(5):2002;557-567.
7. Chen S., Foias C., Holm D.D., Olson E.J., Titi E.S., Wynne S. The Camassa-Holm equations as a closure model for turbulent channel and pipe flows. Phys. Rev. Lett. 81:1998;5338-5341.
8. Dullin H.R., Gottwald G., Holm D.D. An integrable shallow water equation with linear and nonlinear dispersion. Phys. Rev. Lett. 87(19):2001;194501-194504.
9. Foias C., Holm D.D., Titi E. The Navier-Stokes-alpha model of fluid turbulence. Physica D. 152:2001;505-519.
10. Liu Z., Qian T. Peakons and their bifurcation in a generalized Camassa-Holm equation. Int. J. Bifur. Chaos. 11:2001;781-792.
11. Tian L, Yin J. Compacton solutions in generalized Camassa-Holm equation. Physica D, in press.
12. Rosenau P., Hyman J.M. Compactons: solitons with finite wavelength. Phys. Rev. Lett. 70(5):1993;564-566.
13. Wazwaz A.M. Compactons dispersive structures for varians of the. k(n,n) and the KP equations Chaos, Solitons & Fractals. 13:2002;1053-1062.
14. Yan Z. New families of solitons with compact support for Boussinesq-like. B(m,n) equations with fully nonlinear dispersion Chaos, Solitons & Fractals. 14:2002;1151-1158.
15. Yan Z., Bluman G. New compacton soliton solutions and solitary patterns solutions of nonlinearly dispersive Boussinesq equations. Comput. Phys. Commun. 149:2002;11-18.
16. Zhang Y., Zheng H. Two types traveling wave solutions in Burgers-KdV equation. Appl. Math. Mech. 21(10):2000;1009-1011.
17. Cheng L., Liang C. Soliton theory and application. 1997;Xidian University Press.
18. Ding D, Tian L. Attractor and its dimensional estimate in dissipative Camassa-Holm equation. J Math Phys, in press.