Mathematics and Statistics 1(3): 162-166, 2013 DOI: 10.13189/ms.2013.010308 http://www.hrpub.org A New Extended (G ′ /G)-Expansion Method to Find Exact Traveling Wave Solutions of Nonlinear Evolution Equations Harun-Or-Roshid 1 , Md. Nur Alam 1 , M. F. Hoque 1,∗ , M. Ali Akbar 2 1 Department of Mathematics Pabna University of Science and Technology, Bangladesh 2 Department of Applied Mathematics University of Rajshahi, Bangladesh * Corresponding Author: fazlul math@yahoo.co.in Copyright c ⃝2013 Horizon Research Publishing All rights reserved. Abstract In this paper, we propose a new extended (G ′ /G)-expansion method to construct exact traveling wave solutions for nonlinear evolution equations. To check the validity and effectiveness of our method, we imple- ment it to the (2+1)-dimensional typical breaking soliton equation.The results that we get are more general and successfully recover most of the previously known solutions which have been found by other sophisticated methods. Many of these solution are found for the first time. Moreover, our method is direct, concise, elementary, effective and can be used for many other nonlinear evolution equations. Keywords new extended (G ′ /G)-expansion method, the (2+1)-dimensional typical breaking soliton equation, traveling wave solutions Mathematics Subject Classification: 35C07, 35C08, 35P99 1 Introduction Nonlinear phenomena play a vital role in applied mathematics, physics and engineering branches. Most of the complex nonlinear phenomena in plasma physics, fluid dynamics, chemistry, biology, mechanics, elastic media and optical fibers etc. can be explained by nonlinear evolution equations(NLEEs). When we want to understand the physical mechanism of the phenomena, exact solutions have to be explored. Recently, a number of prominent mathematicians and physicists have worked out on this interesting area of research to obtain exact solutions of NLEEs using symbolical computer programs such as Maple, Matlab, Mathematica that facilitate complex and tedious algebraical computations. For example, the wave phenomena observed in fluid dynamics [4, 14], plasma and elastic media [5, 12] and optical fibers [11, 19] etc. Some of the existing powerful methods for deriving exact solutions of NLEEs are Backlund transformation method [10], Darboux Transformations [8], tanh-function method [18], Exp-function method [7] and so on. Wang et al. [17] firstly proposed the (G ′ /G)-expansion method, then many diverse group of researchers extended this method by different names like a new (G ′ /G)-expansion method [3], extended (G ′ /G)-expansion method [2, 15], generalized (G ′ /G)-expansion method [13], modified simple equation method [6] with different auxiliary equations. Zayed [20] established extended (G ′ /G)-expansion method for solving the (3+1)-dimensional NLEEs in mathematical physics. In this expose, the motivation of our method is to add new more general traveling wave solutions in the lit- erature to interpret complex mechanism of different NLEEs. We apply this method to the (2+1)-dimensional typical breaking soliton equation. The performances will encourage other researchers to apply it in other nonlinear evolution equations for searching traveling wave solutions.