BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS FOR A GENERALIZED HIROTA-SATSUMA COUPLED KdV SYSTEM

Jihong Rong (P. R. China), Shengqiang Tang (P. R. China), Wentao Huang (P. R. China) and Zhaojuan Wang (P. R. China)

Received October 21, 2007

References:

[1] S. N. Chow and J. K. Hale, Method of Bifurcation Theory, Springer-Verlag, New York, 1981. [2] L. Debnath, Nonlinear Partial Differential Equations for Scientists and Engineers, Birkhauser, Boston, 1997. [3] E. Fan, Soliton solutions for a generalized Hirota-Satsuma coupled KdV equation and a coupled MKdV equation, Phys. Lett. A 282 (2001), 18-22. [4] D. D. Ganji and M. Rafei, Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method, Phys. Lett. A 356 (2006), 131-137. [5] J. Guckenheimer and P. J. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York, 1985. [6] J. H. He and X. H. Wu, Chaos, Solitons and Fractals 29(1) (2006), 108-113. [7] R. Hirota and J. Satsuma, Soliton solutions of a coupled Korteweg-de Vries equation, Phys. Lett. A 85 (1981), 407-408. [8] D. Kaya, Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation, Appl. Math. Comput. 147 (2004), 69-78. [9] W. Malfliet, Am. J. Phys. 60 (1992), 650. [10] L. Perko, Differential Equations and Dynamical Systems, Springer-Verlag, New York, 1991. [11] Y. T. Wu, X. G. Geng, X. B. Hu and S. M. Zhu, A generalized Hirota-Satsuma coupled Korteweg-de Vries equation and Miura transformations, Phys. Lett. A 255 (1999), 259-264. [12] E. M. E. Zayed, H. A. Zedan and K. A. Gepreel, On the solitary wave solutions for nonlinear Hirota-Satsuma coupled KdV of equations, Chaos, Solitons and Fractals 22 (2004), 285-303.

Keywords and phrases: solitary wave, kink and anti-kink waves, periodic wave, H-S KdV system.