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Exact traveling wave solutions of the Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation. (English) Zbl 1193.35199
Summary: The bifurcation method for dynamical systems is employed to investigate traveling wave solutions in the $\left(2+1\right)$-dimensional Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation. Under some parameter conditions, exact solitary wave solutions and kink wave solutions are obtained.
##### MSC:
 35Q53 KdV-like (Korteweg-de Vries) equations 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies 37K50 Bifurcation problems (infinite-dimensional systems) 35C08 Soliton solutions of PDE
##### References:
 [1] Wazwaz, A. M.: Compact and noncompact physical structures for the ZK – BBM equation, Appl. math. Comp. 169, No. 1, 713-725 (2005) · Zbl 1078.35527 · doi:10.1016/j.amc.2004.09.062 [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 fractals 38, No. 5, 1505-1516 (2008) · Zbl 1154.35443 · doi:10.1016/j.chaos.2007.01.135 [3] Abdou, M. A.: The extended F-expansion method and its application for a class of nonlinear evolution equations, Chaos solitons fractals 31, No. 1, 95-104 (2007) · Zbl 1138.35385 · doi:10.1016/j.chaos.2005.09.030 [4] Abdou, M. A.: Exact periodic wave solutions to some nonlinear evolution equations, Int. J. Nonlinear sci. 6, No. 2, 145-153 (2008) [5] Mahmoudi, J.; Tolou, N.; Khatami, I.; Barari, A.; Ganji, D. D.: Explicit solution of nonlinear ZK – BBM wave equation using exp-function method, J. appl. Sci. 8, No. 2, 358-363 (2008) [6] Li, J. B.; Liu, Z. R.: Smooth and non-smooth traveling waves in a nonlinearly dispersive equation, Appl. math. Modell. 25, No. 1, 41-56 (2000) · Zbl 0985.37072 · doi:10.1016/S0307-904X(00)00031-7 [7] Li, J. B.; Zhang, L. J.: Bifurcations of traveling wave solutions in generalized Pochhammer – chree equation, Chaos solitons fractals 14, 581-593 (2002) · Zbl 0997.35096 · doi:10.1016/S0960-0779(01)00248-X [8] 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 [9] Song, M.; Yang, C. X.; Zhang, B. G.: Exact solitary wave solutions of the kadomtsov-Petviashvili – benjamin-bona-Mahony equation, Appl. math. Comput. (2009) [10] Song, M.; Cai, J. H.: Solitary wave solutions and kink wave solutions for a generalized Zakharov-Kuznetsov equation, Appl. math. Comput. (2009) [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)