Journal of Applied Sciences1812-56541812-5662orgz10.3923/jas.2006.2856.2865TangShengqiangWentao Huang122006614In this study, the generalized special Dodd-Bullough-Mikhailov Equations u_{tt}-u_{xx }= αe^{mu} + βe^{-nu} is studied. The existence of periodic wave and unbounded wave solutions of this equation is proved by using the method of bifurcation theory of dynamical systems. Some exact explicit parametric representations of the above traveling solutions are also obtained.]]>Chow, S.N. and J.K. Hale,1981Li, J. and L. Zhenrong,2000Li, J. and L. Zhenrong,2002Li, J. and G. Chen,2005Wazwaz, A.M.,2005