scholarly journals New infinite sequence exact solutions of nonlinear evolution equations with variable coefficients by the second kind of elliptic equation

2011 ◽  
Vol 60 (9) ◽  
pp. 090201
Author(s):  
Taogetusang ◽  
Narenmandula
Keyword(s):  
Elliptic Equation ◽  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Infinite Sequence ◽  
Variable Coefficients ◽  
Nonlinear Evolution Equations

Application of the Exp-Function Method for Solving Some Evolution Equations with Nonlinear Terms of any Orders

2010 ◽  
Vol 65 (12) ◽  
pp. 1039-1044 ◽  
Author(s):  
Abdelhalim Ebaid
Keyword(s):  
Exact Solutions ◽  
Function Method ◽  
Evolution Equations ◽  
Burgers Equation ◽  
Nonlinear Evolution ◽  
Vries Equation ◽  
Variable Coefficients ◽  
Nonlinear Evolution Equations ◽  
Full Agreement ◽  
Different Types

In this paper, suitable transformations and a so-called exp-function method are used to obtain different types of exact solutions for some nonlinear evolution equations with variable coefficients and nonlinear terms of any orders. The Korteweg-de Vries equation and the Burgers equation with nonlinear terms of any orders are chosen to show how to apply the exp-function method for these kinds of nonlinear equations. These exact solutions are in full agreement with the previous results obtained by Ebaid and by Zhu.

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 Some Methods about Finding the Exact Solutions of Nonlinear Modified BBM Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Fan Niu ◽  
Jianming Qi ◽  
Zhiyong Zhou
Keyword(s):  
Exact Solutions ◽  
Rational Function ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Complex Method ◽  
First Time ◽  
Bbm Equation

Finding exact solutions of nonlinear equations plays an important role in nonlinear science, especially in engineering and mathematical physics. In this paper, we employed the complex method to get eight exact solutions of the modified BBM equation for the first time, including two elliptic function solutions, two simply periodic solutions, and four rational function solutions. We used the exp − ϕ z -expansion methods to get fourteen forms of solutions of the modified BBM equation. We also used the sine-cosine method to obtain eight styles’ exact solutions of the modified BBM equation. Only the complex method can obtain elliptic function solutions. We believe that the complex method presented in this paper can be more effectively applied to seek solutions of other nonlinear evolution equations.

Application of the Subequation Method to Some Differential Equations of Time-Fractional Order

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Ahmet Bekir ◽  
Esin Aksoy
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Order ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
New Exact Solutions

The main goal of this paper is to develop subequation method for solving nonlinear evolution equations of time-fractional order. We use the subequation method to calculate the exact solutions of the time-fractional Burgers, Sharma–Tasso–Olver, and Fisher's equations. Consequently, we establish some new exact solutions for these equations.

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