Hasibun Naher

New traveling wave solutions of the higher dimensional nonlinear partial differential equation by the exp-function method

This article was published in the Journal of Applied Mathematics [© 2012 Hasibun Naher et al.] and the definite version is available at :http://dx.doi.org/10.1155/2012/575387 The Journals website is at:https://www.hindawi.com/journals/jam/2012/575387/

New approach of (G′G)-expansion method and new approach of generalized (G′G)-expansion method for nonlinear evolution equation

In 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.

The exp-function method for new exact solutions of the nonlinear partial differential equations

This article was published in the International Journal of Physical Sciences [© 2011 Academic Journals] and the definite version is available at : 10.5897/IJPS11.1026

The (′/)-Expansion Method for Abundant Traveling Wave Solutions of Caudrey-Dodd-Gibbon Equation

We 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.

Generalized and Improved (G′/G)-Expansion Method for (3+1)-Dimensional Modified KdV-Zakharov-Kuznetsev Equation

The generalized and improved -expansion method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. In this article, we investigate the higher dimensional nonlinear evolution equation, namely, the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation via this powerful method. The solutions are found in hyperbolic, trigonometric and rational function form involving more parameters and some of our constructed solutions are identical with results obtained by other authors if certain parameters take special values and some are new. The numerical results described in the figures were obtained with the aid of commercial software Maple.

Some new traveling wave solutions of the nonlinear reaction diffusion equation by using the improved (G′/G)-expansion method

We 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.

The improved (G'/G) -expansion method for the (2+1)-dimensional modified Zakharov-Kuznetsov equation

we apply the improved (𝐺/𝐺)-expansion method for constructing abundant new exact traveling wave solutions of the (2

New traveling wave solutions by the extended generalized Riccati equation mapping method of the (2 + 1) -dimensional evolution equation

The generalized Riccati equation mapping is extended with the basic -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

Abundant traveling wave solutions of the compound KdV-Burgers equation via the improved (G′/G)-expansion method

In 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.

Extended generalized Riccati equation mapping method for the fifth-order Sawada-Kotera equation

In this article, the generalized Riccati equation mapping together with the basic (G′/G)-expansion method is implemented which is advance mathematical tool to investigate nonlinear partial differential equations. Moreover, the auxiliary equation G′(ϕ) = h + f G(ϕ) + g G2(ϕ) is used with arbitrary constant coefficients and called the generalized Riccati equation. By applying this method, we have constructed abundant traveling wave solutions in a uniform way for the Sawada-Kotera equation. The obtained solutions of this equation have vital and noteworthy explanations for some practical physical phenomena.