Harun-Or Roshid

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(−ϕ(ξ))-expansion method

In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(−ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

New extended (G’/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation

In this article, a new extended (G′/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G'/G)-expansion method

Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (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, trigonometric, and rational functions. It is shown that the new approach of generalized (G′/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations in mathematical physics and engineering.PACS05.45.Yv, 02.30.Jr, 02.30.Ik

Application of Exp(())-expansion Method to Find the Exact Solutions of Nonlinear Evolution Equations

In this paper, we explore new applications of the )) ( exp(    -expansion method for finding exact traveling wave solutions of generalized Klein-Gordon Equation and right-handed nc-Burgers equation. By means of this method three new solutions of each equations is obtained including the hyperbolic functions, exponential functions and rational function solutions. The proposed method is very effective, efficient and applicable mathematical tools for nonlinear evolution equations (NLEEs). So this method can be used for many other nonlinear evolution equations.

Exact and explicit traveling wave solutions to two nonlinear evolution equations which describe incompressible viscoelastic Kelvin-Voigt fluid

Two nonlinear evolution equations, namely the Kadomtsev-Petviashvili (KP) equation which describes the dynamics of soliton and nonlinear wave in the field of fluid dynamics, plasma physics and the Oskolkov equation which describes the dynamics of an incompressible visco-elastic Kelvin-Voigt fluid are investigated. We deliberate exact traveling wave solutions, specially kink wave, cusp wave, periodic breather waves and periodic wave solutions of the models applying the modified simple equation method. The solutions can be expressed explicitly. The dynamics of obtained wave solutions are analyzed and illustrated in figures by selecting appropriate parameters. The modified simple equation method is reliable treatment for searching essential nonlinear waves that enrich variety of dynamic models arises in engineering fields.

Application of Generalized Kudryashov Method to the Burger Equation

The paper considers the Burger equation to search new solutions win the help of generalized Kudryashov method. As a result we obtained exponential type solution involving kink soliton, singular kink soliton and multi soliton solutions with some free parameters. It has been shown that the method provides a powerful mathematical tool for solving non-linear wave equations in mathematical physics and engineering problems.

A Note on Novel ( G'/G) -expansion Method in Nonlinear Physics

Abstract: The exact solutions of nonlinear evolution equations (NLEEs) play a critical role to make known the internal mechanism of complex physical phenomena. In this article, we construct the traveling wave solutions of the (1+1)-dimensional KdV equation and the Banjamin-Ono equation by means of the novel (G0/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, trigonometric and rational functions. It is shown that the novel (G0/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations.