ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.8(2009) No.4,pp.428-434 Travelling Wave Solutions for the Generalized (2+1)-Dimensional ZK-MEW Equation Alaattin Esen ∗ , Selc ¸uk Kutluay Department of Mathematics, In ¨ on¨ u University, 44280 Malatya, Turkey (Received 11 March 2009, accepted 14 July 2009) Abstract:In this paper, we construct exact travelling wave solutions for the generalized (2+1)- dimensional ZK-MEW equation by using the solutions of an auxiliary ordinary differential equation given by Sirendaoreji [1]. It is shown that some solutions obtained in this study are new solutions which have not been reported yet. Keywords:auxiliary equation method; travelling wave solutions; generalized ZK-MEW equa- tion 1 Introduction A large number of equations in many areas of applied mathematics, physics and engineering appear as nonlinear wave equations. One of the most important one-dimensional nonlinear wave equations is the KdV equation + + =0 which describes the evolution of weakly nonlinear and weakly dispersive wave used in various fields such as solid state physics, plasma physics, fluid physics and quantum field theory [2,3]. One of the best known 2-dimensional generalizations of the KdV equation is Zakharov-Kuznetsov (ZK) equation [4] in the form + +( + ) =0 which governs the behaviour of weakly nonlinear ion-acoustic in a plasma comprising cold-ions and hot isothermal electrons in the presence of a uniform magnetic field [5-10]. The ZK equation is not integrable by the inverse scattering transform method. Shivamoggi [11] showed that the ZK equation has the Painleve property. The modified equal width (MEW) equation is of the form + ( 3 ) − =0 which appears in many physical applications [12-15]. The generalized form of the MEW equation in the ZK sense [16] is given by + ( ) +( + ) =0. (1) It is natural to call this equation as the ZK-MEW equation. Wazwaz [16] studied Eq. (1) using the sine-cosine method and the tanh technique. In recent years, much efforts have been spent on the construction of exact travelling wave solutions of these types equations and many powerful methods have been presented such as the inverse scattering ∗ Corresponding author. Tel.: +90-422-3410010; fax: +90-422-3410037. E-mail address: aesen@inonu.edu.tr Copyright c ⃝World Academic Press, World Academic Union IJNS.2009.12.30/299