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Exact solitary wave solutions of the Kadomtsov-Petviashvili-Benjamin-Bona-Mahony equation. (English) Zbl 1203.35245
Summary: Bifurcation method of dynamical systems is employed to investigate bifurcation of solitary waves in the nonlinear dispersive Kadomtsov-Petviashvili-Benjamin-Bona-Mahony equation. Numbers of solitary waves are given for each parameter condition. Under some parameter conditions, exact solitary wave solutions are obtained.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
37K50Bifurcation problems (infinite-dimensional systems)
35B30Dependence of solutions of PDE on initial and boundary data, parameters
35C08Soliton solutions of PDE
References:
[1]Wazwaz, A. M.: Exact solutions of compact and noncompact structures for the KP-BBM equation, Appl. math. Comput. 169, No. 1, 700-712 (2005)
[2]Wazwaz, A. M.: The extended tanh method for new compact and noncompact solutions for the KP-BBM and the ZK-BBM equations, Chaos solitons fract. 38, No. 5, 1505-1516 (2008) · Zbl 1154.35443 · doi:10.1016/j.chaos.2007.01.135
[3]Abdou, M. A.: Exact periodic wave solutions to some nonlinear evolution equations, Int. J. Nonlinear sci. 6, No. 2, 145-153 (2008)
[4]Li, J. B.; Liu, Z. R.: Smooth and non-smooth traveling waves in a nonlinearly dispersive equation, Appl. math. Model. 25, No. 1, 41-56 (2000) · Zbl 0985.37072 · doi:10.1016/S0307-904X(00)00031-7
[5]Liu, Z. R.; Qian, T. F.: Peakons and their bifurcation in a generalized Camassa – Holm equation, Int. J. Bifur. chaos 11, No. 3, 781-792 (2001) · Zbl 1090.37554 · doi:10.1142/S0218127401002420
[6]Liu, Z. R.; Yang, C. X.: The application of bifurcation method to a higher-order KdV equation, J. math. Anal. appl. 275, No. 1, 1-12 (2002) · Zbl 1012.35076 · doi:10.1016/S0022-247X(02)00210-X
[7]Zhang, W. L.: Solitary wave solutions and kink wave solutions for a generalized PC equation, Acta. math. Appl. sin., English series 21, No. 1, 125-134 (2005) · Zbl 1084.35541 · doi:10.1007/s10255-005-0223-1
[8]Tang, M. Y.; Zhang, W. L.: Four types of bounded wave solutions of CH-γ equation, Sci. China ser. A: math. 50, No. 1, 132-152 (2007) · Zbl 1117.35310 · doi:10.1007/s11425-007-2042-8
[9]Liu, Z. R.; Ouyang, Z. Y.: A note on solitary wave for modified forms of Camassa – Holm and Degasperis – Procesi equation, Phys. lett. A 366, No. 4 – 5, 377-381 (2007) · Zbl 1203.35234 · doi:10.1016/j.physleta.2007.01.074
[10]Wang, Q. D.; Tang, M. Y.: New exact solutions for two nonlinear equations, Phys. lett. A 372, No. 17, 2995-3000 (2008) · Zbl 1220.37069 · doi:10.1016/j.physleta.2008.01.012
[11]Chow, S. N.; Hale, J. K.: Method of bifurcation theory, (1982)
[12]Guckenheimer, J.; Homes, P.: Nonlinear oscillations, Dynamical systems and bifurcations of vector fields (1999)