New type of exact solutions of nonlinear evolution equations via the new Sine–Poisson equation expansion method

2005 ◽  
Vol 26 (4) ◽  
pp. 1081-1086 ◽  
Author(s):  
Yuqin Yao
Keyword(s):  
Exact Solutions ◽  
Poisson Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
New Type

scholarly journals New Jacobi Elliptic Function Solutions for the Zakharov Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yun-Mei Zhao
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobi Elliptic Function

A generalized(G′/G)-expansion method is proposed to seek the exact solutions of nonlinear evolution equations. Being concise and straightforward, this method is applied to the Zakharov equations. As a result, some new Jacobi elliptic function solutions of the Zakharov equations are obtained. This method can also be applied to other nonlinear evolution equations in mathematical physics.

scholarly journals Further Results about Traveling Wave Exact Solutions of the (2+1)-Dimensional Modified KdV Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Yang Yang ◽  
Jian-ming Qi ◽  
Xue-hua Tang ◽  
Yong-yi Gu
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Mkdv Equation ◽  
Nonlinear Evolution Equations ◽  
Complex Method ◽  
Modified Kdv Equation

We used the complex method and the exp(-ϕ(z))-expansion method to find exact solutions of the (2+1)-dimensional mKdV equation. Through the maple software, we acquire some exact solutions. We have faith in that this method exhibited in this paper can be used to solve some nonlinear evolution equations in mathematical physics. Finally, we show some simulated pictures plotted by the maple software to illustrate our results.

Application of Improved (G′/G)–Expansion Method to Traveling Wave Solutions of Two Nonlinear Evolution Equations

2012 ◽  
Vol 4 (1) ◽  
pp. 122-130 ◽  
Author(s):  
Xiaohua Liu ◽  
Weiguo Zhang ◽  
Zhengming Li
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Nonlinear Evolution Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
The Other ◽  
Wave Solutions

AbstractIn this work, the improved (G′/G)-expansion method is proposed for constructing more general exact solutions of nonlinear evolution equation with the aid of symbolic computation. In order to illustrate the validity of the method we choose the RLW equation and SRLW equation. As a result, many new and more general exact solutions have been obtained for the equations. We will compare our solutions with those gained by the other authors.

AN EFFICIENT METHOD FOR FINDING THE EXACT SOLUTION OF NONLINEAR EVOLUTION EQUATIONS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1703-1706 ◽  
Author(s):  
XIQIANG ZHAO ◽  
DENGBIN TANG ◽  
CHANG SHU
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

In this paper, based on the idea of the homogeneous balance method, the special truncated expansion method is improved. The Burgers-KdV equation is discussed and its many exact solutions are obtained with the computerized symbolic computation system Mathematica. Our method can be applied to finding exact solutions for other nonlinear partial differential equations too.

scholarly journals F-Expansion Method and New Exact Solutions of the Schrödinger-KdV Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ali Filiz ◽  
Mehmet Ekici ◽  
Abdullah Sonmezoglu
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Jacobi Elliptic Function ◽  
Weierstrass Elliptic Function ◽  
New Exact Solutions

F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulusmof Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics.

scholarly journals Application of Exp(())-expansion Method to Find the Exact Solutions of Nonlinear Evolution Equations

2014 ◽  
Vol 9 (6) ◽  
pp. 106-113 ◽  
Author(s):  
Selina Akter ◽  
◽  
Harun-Or- Roshid ◽  
Md. Nur Alam ◽  
Nizhum Rahman ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Expansion Method ◽  
Nonlinear Evolution Equations

Extended Jacobian Elliptic Function Expansion Method and Its Applications in Mathematical Physics

2016 ◽  
pp. 3585-3592
Author(s):  
Mostafa Khater
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Validity And Reliability ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to some nonlinear evolution equations which play an important role inmathematical physics.

Geometrical Properties and Exact Solutions of Three (3+1)-Dimensional Nonlinear Evolution Equations in Mathematical Physics Using Different Expansion Methods

2019 ◽  
pp. 1-19
Author(s):  
A. R. Shehata ◽  
Safaa S. M. Abu-Amra
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Shallow Water Equation ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Wave Solutions

In this article, A Variation of -Expansion Method and -Expansion Method have been applied to find the traveling wave solutions of the (3+1)-dimensional Zakhrov-Kuznetsov (ZK) equation, the (3+1)-dimensional Potential-YTSF Equation and the (3+1)-dimensional generalized Shallow water equation. The efficiency of these methods for finding the exact solutions have been demonstrated. As a result, some new exact traveling wave solutions are obtained which include solitary wave solutions. It is shown that the methods are effective and can be used for many other Nonlinear Evolution Equations (NLEEs) in mathematical physics. In this article, A Variation of -Expansion Method and -Expansion Method have been applied to find the traveling wave solutions of the (3+1)-dimensional Zakhrov-Kuznetsov (ZK) equation, the (3+1)-dimensional Potential-YTSF Equation and the (3+1)-dimensional generalized Shallow water equation. The efficiency of these methods for finding the exact solutions have been demonstrated. As a result, some new exact traveling wave solutions are obtained which include solitary wave solutions. It is shown that the methods are effective and can be used for many other Nonlinear Evolution Equations (NLEEs) in mathematical physics.

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