Publisher : Department of Mathematics, Kyungpook National University
DOI : 10.5666/KMJ.2009.49.1.081
Title & Authors
Application of Bifurcation Method to a Generalized Modified Boussinesq Equation Song, Ming; Yang, Chengxi;
Bifurcation method of dynamical systems is employed to investigate exact solitary wave solutions and kink wave solutions in the generalized modified Boussinesq equation. Under some parameter conditions, their explicit expressions are obtained. Some previous results are extended.
bifurcation of phase portraits;solitary wave solutions;Kink wave solutions;
Exact solitary wave solutions of the generalized (2+1) dimensional Boussinesq equation, Applied Mathematics and Computation, 2010, 217, 7, 3557
W. G. Zhang, Q. S. Chang, E. G. Fan, Methods of judging shape of solitary wave and solution formulae for some evolution equations with nonlinear terms of high order, J. Math. Anal. Appl., 287(2003), 1-18.
D. Kaya, The exact and numerical solitary-wave solutions for generalized modified Boussinesq equation, Phys. Lett., 348(2006) 244-250.
P. A. Clarkson, R. J. Leveque, R. Saxton, Solitary wave interactions in elastic rods, Stud. Appl. Math., 75(1986), 95-122.
I. L. Bogolubsky, Some examples of inelastic solition interaction, Comput. Phys. Commun., 13(1977), 149-155.
A. Parker, On exact solutions of the regularied long-wave equation: A direct approach to partially integrable equation, 1. solitary wave and solutions, J. Math. Phys., 36(1995), 3498-3505.
W. G. Zhang, W. X. Ma, Explicit solitary-wave solutions to generalized Pochhammer-Chree equations, Appl. Math. Mech., 20(1999), 666-674.
J. B. Li, L. J. Zhang, Bifurcations of traveling wave solutions in generalized Pochhammer-Chree equation, Chaos Solitons Fractals, 14(2002), 581-593.
W. L. Zhang, Solitary wave solutions and kink wave solutions for a generalized PC equation, Acta. Math. Appl. Sinica, English Series 21(2005), 125-134.
M. Rafei, D. D. Ganji, H. R. Mohammadi Daniali, H. Pashaei, Application of homotopy perturbation method to the RLM and generalized modified Boussinesq equations, Phys. Lett., 364(2007), 1-6.
Z. R. Liu, Z. Y. Ouyang, A note on solitary wave for modified forms of Camassa-Holm and Degasperis-procesi equation, Phys. Lett., 366(2007), 377-381.
T. Jiang, Z. Y. Yang, Z. R. Liu, Bounded traveling wave soultion of a nolinear equation, Kyungpook Math J., 43(2003), 113-125
S. N. Chow, J. K. Hale, Method of bifurcation theory, Springer-verlag, New York, 1982.
J. Guckenheimer, P. Homes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-verlag, New York, 1999.