A Generalized and Improved G′/G -Expansion Method for Nonlinear Evolution Equations

نویسندگان

  • M. Ali Akbar
  • E. M. E. Zayed
  • Jaromir Horacek
چکیده

A generalized and improved G′/G -expansion method is proposed for finding more general type and new travelling wave solutions of nonlinear evolution equations. To illustrate the novelty and advantage of the proposed method, we solve the KdV equation, the Zakharov-KuznetsovBenjamin-Bona-Mahony ZKBBM equation and the strain wave equation in microstructured solids. Abundant exact travelling wave solutions of these equations are obtained, which include the soliton, the hyperbolic function, the trigonometric function, and the rational functions. Also it is shown that the proposed method is efficient for solving nonlinear evolution equations in mathematical physics and in engineering.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Application of the new extended (G'/G) -expansion method to find exact solutions for nonlinear partial differential equation

In recent years, numerous approaches have been utilized for finding the exact solutions to nonlinear partial differential equations. One such method is known as the new extended (G'/G)-expansion method and was proposed by Roshid et al. In this paper, we apply this method and achieve exact solutions to nonlinear partial differential equations (NLPDEs), namely the Benjamin-Ono equation. It is est...

متن کامل

The Generalized and Improved (G'/G)-Expansion Method with the Jacobi Elliptic Equation for Exact Solutions of Nonlinear Evolution Equations

Submitted: Mar 2, 2013; Accepted: Apr 10, 2013; Published: Jun 10, 2013 Abstract: In this article, we present a variant approach of the generalized and improved (G'/G)–expansion method and construct some new exact traveling wave solutions with free parameters of the nonlinear evolution equations, via the Painleve integrable Burgers equation, the Boiti-Leon-Pempinelle equation and the Pochhammer...

متن کامل

Generalized G ′ G - Expansion Method and its Applications *

In this paper,the traditional G′/G-expansion method is improved and a generalized G′/G-expansion method is proposed to seek exact solutions of nonlinear evolution equations.And we choose Benjamin-Bona-Mahony equation,(2+1) dimensional generalized Zakharov-Kuznetsov equation and variant Bousinessq equations to illustrate the validity and advantages of the proposed method.It is shown that the pro...

متن کامل

Exact travelling wave solutions for some complex nonlinear partial differential equations

This paper reflects the implementation of a reliable technique which is called $left(frac{G'}{G}right)$-expansion  ethod for  constructing exact travelling wave solutions of nonlinear partial  differential equations. The proposed algorithm has been successfully tested on two two selected equations, the balance numbers of which are not positive integers namely Kundu-Eckhaus equation and  Derivat...

متن کامل

Stochastic differential inclusions of semimonotone type in Hilbert spaces

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2014