Bifurcations of travelling wave solutions in a new integrable equation with peakon and compactons

Chaos, Solitons and Fractals

Volumn 27, Issue 2, 2006, Pages 413-425

  Shen, Jianwei ^a,b   Xu, Wei ^a   Li, Wei ^a  

^a NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

^b XUCHANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CLASSIFICATION (OF INFORMATION); COMPUTATIONAL METHODS; DISPERSIONS; PARAMETER ESTIMATION;

BIFURCATION THEORY; DEGASPERIS-PROCESI EQUATIONB (DPE); NONLINEAR WAVE EQUATIONS; TRAVELLING WAVE SOLUTIONS;

NONLINEAR EQUATIONS;

EID: 22844440384     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.04.020     Document Type: Article

References (19)

1. A.A. Andronov Theory of bifurcations of dynamical systems on a plane 1973 Wiley New York
2. P.F. Byrd, and M.D. Friedman Handbook of elliptic integrals for engineers and physicist 1971 Springer-Verlag New York
3. S.N. Chow, and J.K. Hale Method of bifurcation theory 1981 Springer-Verlag New York
4. L. Perko Differential equations and dynamical systems 1991 Springer-Verlag New York
5. R. Camassa, and D.D. Holm An integrable shallow water equation with peaked solitons Phys Rev Lett 71 1993 1661 1664
6. A. Degasperis A new integrable equation with peakon solutions Theor Math Phys 133 2 2002 1461 1472
7. J. Guckenheimer, and P.J. Holmes Nonlinear oscillations, dynamical systems and bifurcations of vector fields 1983 Springer-Verlag New York
8. J.B. Li, and Z.R. Liu Smooth and non-smooth travelling waves in a nonlinearly dispersive equation Appl Math Model 25 2000 41 56
9. J.B. Li, and Z.R. Liu Travelling waves solutions for a class of nonlinear dispersive equations Chin Ann Math Ser B 23 3 2002 397 418
10. J.B. Li, and J.W. Shen Travelling solutions in a model of the Helix Polypeptide chains Chaos, Solitons & Fractal 20 2004 827 841
11. J.B. Li, and H. Li Bifurcations of travelling wave solutions for the generalized Kadomtsev-Petviashili equation Chaos, Solitons & Fractals 20 2004 725 734
12. J.B. Li, and J.X. Zhang Bifurcations of travelling wave solutions for the generalization form of the modified KdV equation Chaos, Solitons & Fractals 24 2004 899 913
13. Y.A. Li, and P.J. Olver Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system I: Compactons and peakons Discrete Contin Dyn Syst 4 1997 419 432
14. Y.A. Li, and P.J. Olver Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system II: Complex analytic behavior and convergence to non-analytic solutions Discrete Contin Dyn Syst 4 1998 159 191
15. A.V. Mikhailov, and V.S. Novikov Perturbative symmetry approach J Phys A: Math Gen 35 2002 4775 4790
16. P. Rosenau, and J.M. Hyman Compactons: solitons with finite wavelenghs Phys Rev Lett 73 1994 305 318
17. J.W. Shen, and W. Xu Bifurcations of smooth and non-smooth travelling wave solution of the Degasperis-Procesi equation Int J Nonlinear Sci Numer Simul 5 4 2004 397 402
18. J.W. Shen, and W. Xu Smooth and non-smooth wave in the nonlinear dispersive Bousinesq equation Chaos, Solitons & Fractals 23 1 2005 117 130
19. J.W. Shen, and W. Xu Travelling solutions in the generalized Hirota-Satsuma coupled Kdv system Appl Math Comput 161 2 2005 365 383