Soliton solutions of the Klein–Gordon–Zakharov equations with power law nonlinearity Houria Triki ⇑ , Noureddine Boucerredj Department of Physics, Faculty of Sciences, Badji Mokhtar University, P.O. Box 12, 23000 Annaba, Algeria article info Keywords: Solitons Klein–Gordon–Zakharov equations Solitary wave ansatz method abstract In this paper, the Klein–Gordon–Zakharov equations which model the interaction between the Langmuir wave and the ion acoustic wave in a high frequency plasma, are considered. To examine the role played by the nonlinear dispersion term in the formation of solitons, a family of the considered equations with power law nonlinearity are investigated. By using two solitary wave ansatze in terms of sec h p ðxÞ and tanh p ðxÞ functions, we find exact ana- lytical bright and dark soliton solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The conditions of existence of solitons are presented. These closed form solutions are helpful to well understand the mechanism of the complicated physical phenomena and dynamical processes modeled by the used model. Ó 2013 Elsevier Inc. All rights reserved. 1. Introduction Two different types of envelope solitons, bright and dark, can propagate in nonlinear dispersive media [1]. The dynamics of such shape-preserving waves is typically described by a certain class of nonlinear partial differential equations (NLPDEs). The best known examples include the cubic nonlinear Schrödinger equation, the Korteweg–de Vries equation, the Sine–Gor- don equation, the Boussinesq equation, etc. The formation of solitons has been regarded as a consequence of the delicate balance between dispersion (or diffraction) and nonlinearity under certain conditions. In real applications, however, it may be difficult to produce such balances [2]. It is worth noting that the existence of soliton solutions depends on the specific nonlinear and dispersive features of the medium [2]. In other words, the key factors, which determine the closed form solu- tions of a given nonlinear evolution equation are the dispersion and nonlinear coefficients which can be constant or variable parameters depending on the physical situation. For this, one may need to know what kind of the existing effects that may contribute for generating soliton pulses in the medium. As is well known, solitons are universal phenomenon, appearing in a great array of contexts such as, for example, non- linear optics, plasma physics, fluid dynamics, semiconductors and many other systems. As a matter of fact, the study of such nonlinear waves has attracted extensive attention. One of the great interests is the problem of finding exact soliton solutions of the integrable nonlinear models. Based on these exact solutions directly, we can accurately analyze the properties of prop- agating soliton pulses in nonlinear physical systems. Towards that goal, many powerful methods to construct exact solutions of NLPDEs have been established and developed, which lead to one of the most excited advances of nonlinear science and theoretical physics [3]. Among these methods we can cite, for example, the subsidiary ordinary differential equation method (sub-ODE for short) [3–5], the coupled amplitude-phase formulation [6], sine–cosine method [7], the Hirota’s bilinear meth- od [8,9], and many others. These methods work even though the Painlevé test of integrability will fail [10]. 0096-3003/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.amc.2013.10.093 ⇑ Corresponding author. E-mail address: houriatriki@yahoo.fr (H. Triki). Applied Mathematics and Computation 227 (2014) 341–346 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc