%0 Journal Article
%T Soliton Solutions of the Klein-Gordon-Zakharov Equation with Power Law Nonlinearity
%A Mehmet Ekici
%A Durgun Duran
%A Abdullah Sonmezoglu
%J ISRN Computational Mathematics
%D 2013
%R 10.1155/2013/716279
%X We introduce a new version of the trial equation method for solving nonintegrable partial differential equations in mathematical physics. Some exact solutions including soliton solutions and rational and elliptic function solutions to the Klein-Gordon-Zakharov equation with power law nonlinearity in (1£¿+£¿2) dimensions are obtained by this method. 1. Introduction In recent years there have been many works on the qualitative research of the global solutions for the Klein-Gordon-Zakharov (KGZ) equations [1¨C4]. Chen considered orbital stability of solitary waves for the KGZ equations in [5]. More recently, some exact solutions for the Zakharov equations are obtained by using different methods [6¨C9]. These solutions are not general and by no means exhaust all possibilities. They are only some particular solutions within some specific parameters choices. The aim of this paper is to find the new and more general explicit and exact special solutions of the KGZ equations. We obtain various of explicit and exact special solutions of the KGZ equations by using the extended trial equation method. These solutions include that of the solitary wave solutions of the singular traveling wave solutions and solitary wave solutions of rational function type. Solving nonlinear evolution equations has become a valuable task in many scientific areas including applied mathematics as well as the physical sciences and engineering. Many powerful methods, such as the Backlund transformation, the inverse scattering method [10], bilinear transformation, the tanh-sech method [11], the extended tanh method, the pseudospectral method [12], the trial function and the sine-cosine method [13], Hirota method [14], tanh-coth method [15, 16], the exponential function method [17], -expansion method [18, 19], homogeneous balance method [20], and the trial equation method [21¨C30] have been used to investigate nonlinear partial differential equations problems. There are a lot of nonlinear evolution equations that are integrated using these and other mathematical methods. In this paper, KGZ equations will be studied by extended trial equation. By virtue of the solitary wave ansatz method, an exact soliton solution will be obtained. The extended trial equation method will be employed to back up our analysis in obtaining exact solutions with distinct physical structures. 2. The Extended Trial Equation Method The main steps of an extended trial equation method for the nonlinear partial differential equations with higher order nonlinearity are outlined as follows. Step 1. For a given nonlinear partial
%U http://www.hindawi.com/journals/isrn.computational.mathematics/2013/716279/