Research Article Conservation Laws and Traveling Wave Solutions of a Generalized Nonlinear ZK-BBM Equation Khadijo Rashid Adem and Chaudry Masood Khalique International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Maikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa Correspondence should be addressed to Chaudry Masood Khalique; masood.khalique@nwu.ac.za Received 25 February 2014; Accepted 3 April 2014; Published 23 April 2014 Academic Editor: Mariano Torrisi Copyright © 2014 K. R. Adem and C. M. Khalique. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We study a generalized two-dimensional nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation, which is in fact Benjamin-Bona-Mahony equation formulated in the ZK sense. Conservation laws for this equation are constructed by using the new conservation theorem due to Ibragimov and the multiplier method. Furthermore, traveling wave solutions are obtained by employing the (  /)-expansion method. 1. Introduction Many phenomena in the real world are oten described by nonlinear evolution equations (NLEEs) and therefore such equations play an important role in applied mathematics, physics, and engineering. Unfortunately, there are no gen- eral methods for obtaining exact solutions for the NLEEs. However, various powerful methods have been developed by many authors to construct exact solutions of NLEEs. hese methods include the inverse scattering transform method [1], Darboux transformation [2], Hirota’s bilinear method [3], B¨ acklund transformation [4], multiple exp- function method [5], the (  /)-expansion method [6], the sine-cosine method [7], the F-expansion method [8], the exp- function expansion method [9], and Lie symmetry method [10]. In addition to exact solutions there is a need to ind conservation laws for the NLEEs. Conservation laws assist in the numerical integration of partial diferential equations [11], theory of nonclassical transformations [12, 13], normal forms, and asymptotic integrability [14]. Recently, conservation laws have been used to derive exact solutions of partial diferential equations [15–17]. In this paper, we analyze one such NLEE, namely, the gen- eralized (2+1)-dimensional nonlinear Zakharov-Kuznetsov- Benjamin-Bona-Mahony (ZK-BBM) equation [18] that is given by   +  + (  )  + (  +  )  = 0. (1) Here, in (1) , , and >1 are real-valued constants. Several authors (see, e.g., the papers [18–23]) have studied this equation. he sine-cosine method, the tanh method, and the extended tanh method were used in [18, 19] and solitary solutions were obtained. Some exact solutions were obtained by Abdou [20, 21] by using the extended F-expansion method and the extended mapping method with symbolic compu- tation. Mahmoudi et al. [22] used the exp-function method to obtain some solitary solutions and periodic solutions. Bifurcation method was used by Song and Yang [23] to obtain exact solitary wave solutions and kink wave solutions. In this paper, conservation laws will be derived for (1) using the new conservation theorem due to Ibragimov [24] and the multiplier method [25]. Moreover, the (  /)- expansion method [6] is used to obtain the traveling wave solutions for (1). Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2014, Article ID 139513, 5 pages http://dx.doi.org/10.1155/2014/139513