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Item The exp-function method for new exact solutions of the nonlinear partial differential equations(© 2011 International Journal of Physical Sciences, 2011) Naher, Hasibun; Abdullah, Farah Aini; Akbar, M. AliIn this article, the exp-function method is used to construct some new exact solitary wave solutions of the sixth-order Boussinesq equation and the regularized long wave equations. These equations play very important role in mathematical physics, engineering sciences and applied mathematics. The exp-function method is a powerful and straightforward mathematical tool for solving nonlinear evolution equations.Item The (G'/G)-expansion method for abundant traveling wave solutions of Caudrey-Dodd-Gibbon equation(© 2011 Mathematical Problems in Engineering, 2011) Naher, Hasibun; Abdullah, Farah Aini; Akbar, M. AliWe construct the traveling wave solutions of the fifth-order Caudrey-Dodd-Gibbon (CDG) equation by the (G'/G) -expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, the trigonometric, and the rational functions. It is shown that the (G ′ / G) -expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations.Item New traveling wave solutions of the higher dimensional nonlinear partial differential equation by the exp-function method(© 2012 Journal of Applied Mathematics, 2012) Naher, Hasibun; Abdullah, Farah Aini; Akbar, M. AliWe construct new analytical solutions of the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.Item New traveling wave solutions of the higher dimensional nonlinear evolution equation by the improved (G′/G) expansion method(© 2012 World Applied Sciences Journal, 2012) Naher, Hasibun; Abdullah, Farah Aini; Akbar, M. AliIn this article, we investigate the nonlinear evolution equation, namely, the (3+l)-dimensional modified KdV-Zakharov-Kuznetsev equation by applying the improved (G′/G)-expansion method to construct some new traveling wave solutions. The obtained solutions are expressed in terms of the hyperbolic, the trigonometric and the rational functions including solitons and periodic solutions. The attained solutions become some special functions when the arbitrary constants taken particular values. It is important to mention that some of our solutions are in good harmony with the existing results which certifies our other solutions.Item The improved (G'/G) -expansion method for the (2+1)-dimensional modified Zakharov-Kuznetsov equation(© 2012 Journal of Applied Mathematics, 2012) Naher, Hasibun; Abdullah, Farah Ainiwe apply the improved (G'/G) -expansion method for constructing abundant new exact traveling wave solutions of the (2+1)-dimensional Modified Zakharov-Kuznetsov equation. In addition, G'' + λ G' + μG = 0 together with b (α) = ∑ q=-w wp q (G'/G) q is employed in this method, where p q (q = 0, ± 1, ± 2,⋯, ± w), λ and μ are constants. Moreover, the obtained solutions including solitons and periodic solutions are described by three different families. Also, it is noteworthy to mention out that, some of our solutions are coincided with already published results, if parameters taken particular values. Furthermore, the graphical presentations are demonstrated for some of newly obtained solutions.Item The modified benjamin-bona-mahony equation via the extended generalized riccati equation mapping method(© 2012 Applied Mathematical Science, 2012) Naher, Hasibun; Abdullah, Farah AiniThe generalized Riccati equation mapping is extended together with the (G'/G) -expansion method and is a powerful mathematical tool for solving nonlinear partial differential equations. In this article, we construct twenty seven new exact traveling wave solutions including solitons and periodic solutions of the modified Benjamin-Bona-Mahony equation by applying the extended generalized Riccati equation mapping method. In this method, G'(μ) = p + rG(μ) + sG 2 (μ) is implemented as the auxiliary equation, where r, s and p are arbitrary constants and called the generalized Riccati equation. The obtained solutions are described in four different families including the hyperbolic functions, the trigonometric functions and the rational functions. In addition, it is worth mentioning that one of newly obtained solutions is identical for a special case with already published result which validates our other solutions.Item Some new traveling wave solutions of the nonlinear reaction diffusion equation by using the improved (G′/G)-expansion method(© 2012 Mathematical Problems in Engineering, 2012) Naher, Hasibun; Abdullah, Farah AiniWe construct new exact traveling wave solutions involving free parameters of the nonlinear reaction diffusion equation by using the improved (G ′ /G)-expansion method. The second-order linear ordinary differential equation with constant coefficients is used in this method. The obtained solutions are presented by the hyperbolic and the trigonometric functions. The solutions become in special functional form when the parameters take particular values. It is important to reveal that our solutions are in good agreement with the existing results.Item Abundant traveling wave solutions of the compound KdV-Burgers equation via the improved (G′/G)-expansion method(© 2012 AIP Advances, 2012) Naher, Hasibun; Abdullah, Farah Aini; Bekir, AhmetIn this article, we investigate the compound KdV-Burgers equation involving parameters by applying the improved (G′/G)-expansion method for constructing some new exact traveling wave solutions including solitons and periodic solutions. The second order linear ordinary differential equation with constant coefficients is used, in this method. The obtained solutions are presented through the hyperbolic, the trigonometric and the rational functions. Further, it is significant to point out that some of our solutions are in good agreement for special cases with the existing results which validates our other solutions. Moreover, some of the obtained solutions are described in the figures.Item New traveling wave solutions by the extended generalized Riccati equation mapping method of the (2 + 1) -dimensional evolution equation(© 2012 Journal of Applied Mathematics, 2012) Naher, Hasibun; Abdullah, Farah AiniThe generalized Riccati equation mapping is extended with the basic (G ′ / G) -expansion method which is powerful and straightforward mathematical tool for solving nonlinear partial differential equations. In this paper, we construct twenty-seven traveling wave solutions for the (2+1)-dimensional modified Zakharov-Kuznetsov equation by applying this method. Further, the auxiliary equation G ′ (η) = w + u G (η) + v G 2 (η) is executed with arbitrary constant coefficients and called the generalized Riccati equation. The obtained solutions including solitons and periodic solutions are illustrated through the hyperbolic functions, the trigonometric functions, and the rational functions. In addition, it is worth declaring that one of our solutions is identical for special case with already established result which verifies our other solutions. Moreover, some of obtained solutions are depicted in the figures with the aid of Maple.Item New approach of (G′G)-expansion method and new approach of generalized (G′G)-expansion method for nonlinear evolution equation(© 2013 AIP Advances, 2013) Naher, Hasibun; Abdullah, Farah AiniIn this article, new (G′G)-expansion method and new generalized (G′G)-expansion method is proposed to generate more general and abundant new exact traveling wave solutions of nonlinear evolution equations. The novelty and advantages of these methods is exemplified by its implementation to the KdV equation. The results emphasize the power of proposed methods in providing distinct solutions of different physical structures in nonlinear science. Moreover, these methods could be more effectively used to deal with higher dimensional and higher order nonlinear evolution equations which frequently arise in many scientific real time application fields.