ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.7(2009) No.4,pp.455-461 Exact Travelling Wave Solutions of Generalized Zakharov Equations with Arbitrary Power Nonlinearities S A El-Wakil 1 ,A R Degheidy 1 ,E M Abulwafa 1 ,M A Madkour 1 ,M T Attia 1 , M A Abdou 1,2 * 1 Theoretical Research Group,Physics Department,Faculty of Science,Mansoura University,35516 Mansoura,Egypt 2 Faculty of Education for Girls,Physics Department,King Kahlid University,Bisha,Saudia Arabia (Received 5 November 2008, accepted 18 April 2009) Abstract: An extended F-expansion method with a computerized symbolic computation for constructing a new exact travelling wave solutions for generalized Zakharov equations with arbitrary power nonlinearitie.As a result, many exact travelling wave solutions are obtained which include new periodic wave solution,trigonometric function solutions and rational solu- tions.The method is straightforward and concise,and it can also be applied to other nonlinear evolution equations arising in mathematical physics. It is worthwhile to mention that the method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics. Keywords:generalized Zakharov equations;F-expansion method;new travelling wave solutions;solitary wave solutions 1 Introduction The investigation of the travelling wave solutions for nonlinear evolution equations arising in mathematical physics plays an important role in the study of nonlinear physical phenomena.The nonlinear evolution equa- tions are major subjects in physical science, appears in various scientific and engineering fields,such as fluid mechanics,plasma physics,optical fibers,biology,solid state physics, chemical kinematics, chemical physics and ochemistry.In the past several decades,new exact solutions may help to find new phenomena.A variety of powerful methods for obtaining the exact solutions of nonlinear evolution equations have been presented [1 − 15]. The application of computer algebra to science has a bright future.In the field of nonlinear science,to find as many and general as possible exact solutions for a nonlinear system is one of the most fundamental and significant study. In the line with the development of computerized symbolic computation,much work has been focused on the various extensions and application of the known algebraic methods to construct the solutions of nonlinear evolution equations. In recent years,numerical analysis [16] has considerably been developed to be used for nonlinear partial equations such as Ginzburg-Landau equation,which is a class of a Schrodinger equation with a nonlinear term [17].This equation governs the finite amplitude evolution of instability waves in a large variety of dissipative systems which are close to criticality. Various forms of Ginzburg-Landau equation arise in hy- drodynamic instability theory: the development of Tollmien-Schlichting waves in plane Poiseuille flows, the nonlinear growth of convection rolls in the Rayleigh-Bnard problem, and appearance of Taylor vortices in the flow between counter rotating circular cylinders [18, 19], The rest of this paper is arranged as follows. Section 2 contains the description of the problem of gen- eralized Zakharov equations.In Section 3, we simply provide the mathematical framework of the extended ∗ Corresponding author. E-mail address:m abdou eg@yahoo.com Copyright c World Academic Press, World Academic Union IJNS.2009.06.30/248