scholarly journals EXACT SOLUTIONS AND CANONICAL REDUCTION OF THE SELF-DUAL YANG MILLS EQUATIONS TO SOME NONLINEAR EVOLUTION EQUATIONS

2014 ◽  
Vol 94 (3) ◽  
Author(s):  
A.R. Shehata ◽  
J.F. Alzaidy
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
The Self ◽  
Yang Mills

NONLINEAR EVOLUTION EQUATIONS AND THE PAINLEVÉ TEST

1992 ◽  
Vol 07 (08) ◽  
pp. 1669-1683 ◽  
Author(s):  
W.-H. STEEB ◽  
N. EULER
Keyword(s):  
Evolution Equations ◽  
Gordon Equation ◽  
Nonlinear Evolution ◽  
Energy Eigenvalue ◽  
Nonlinear Evolution Equations ◽  
The Self ◽  
Painlevé Test ◽  
Yang Mills ◽  
Petviashvili Equation ◽  
Klein Gordon

A survey is given of new results of the Painlevé test and nonlinear evolution equations where ordinary- and partial-differential equations are considered. We study the semiclassical Jaynes-Cumming model, the energy-eigenvalue-level-motion equation, the Kadomtsev-Petviashvili equation, the nonlinear Klein-Gordon equation and the self-dual Yang-Mills equation.

ON THE GENERALIZED TANH METHOD FOR THE (2+1)-DIMENSIONAL BREAKING SOLITON EQUATION

1995 ◽  
Vol 10 (38) ◽  
pp. 2937-2941 ◽  
Author(s):  
BO TIAN ◽  
YI-TIAN GAO
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
The Self ◽  
Solitary Wave Solutions ◽  
Soliton Equation ◽  
Yang Mills ◽  
Wave Solutions ◽  
Tanh Method ◽  
Open Question

There is an open question as to whether or not the recently-proposed tanh method can be modified in order to proceed beyond the traveling or solitary wave solutions for nonlinear evolution equations. On the other hand, the class of the breaking soliton equations, which the self-dual Yang-Mills equation is found to belong to, is of current interest. In this letter, we propose a generalized tanh method, with symbolic computation, to construct a family of soliton-like solutions for a (2+1)-dimensional breaking soliton equation.

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.

scholarly journals A Novel Analytical Technique to Obtain Kink Solutions for Higher Order Nonlinear Fractional Evolution Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Qazi Mahmood Ul Hassan ◽  
Jamshad Ahmad ◽  
Muhammad Shakeel
Keyword(s):  
Differential Equation ◽  
Exact Solutions ◽  
Fractional Derivatives ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Fractional Evolution Equations ◽  
Analytical Technique ◽  
Fractional Complex Transform ◽  
Fifth Order

We use the fractional derivatives in Caputo’s sense to construct exact solutions to fractional fifth order nonlinear evolution equations. A generalized fractional complex transform is appropriately used to convert this equation to ordinary differential equation which subsequently resulted in a number of exact solutions.

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