Notizen: Bäcklund Transformation Groups of Non-Linear Evolution Equations and the Painlevé Property

1983 ◽  
Vol 38 (1) ◽  
pp. 86-87
Author(s):  
W.-H. Steeb ◽  
W. Oevel
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Evolution Equations ◽  
Bäcklund Transformation ◽  
Transformation Groups ◽  
Backlund Transformation ◽  
Linear Evolution ◽  
Painlevé Property ◽  
Non Linear ◽  
Linear Evolution Equations

Abstract We show that the group theoretical reduction of evolution equations which admit Lie-Bäcklund transformation groups does not lead in general to ordinary differential equations with the Painlevé property.

scholarly journals Bäcklund transformations for several cases of a type of generalized KdV equation

2004 ◽  
Vol 2004 (63) ◽  
pp. 3369-3377
Author(s):  
Paul Bracken
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Bäcklund Transformation ◽  
Kdv Equation ◽  
Bäcklund Transformations ◽  
Backlund Transformation ◽  
Generalized Kdv Equation ◽  
Backlund Transformations ◽  
De Vries ◽  
Derivative Term

An alternate generalized Korteweg-de Vries system is studied here. A procedure for generating solutions is given. A theorem is presented, which is subsequently applied to this equation to obtain a type of Bäcklund transformation for several specific cases of the power of the derivative term appearing in the equation. In the process, several interesting, new, ordinary, differential equations are generated and studied.

scholarly journals A direct algorithm of exp-function method for non-linear evolution equations in fluids

2016 ◽  
Vol 20 (3) ◽  
pp. 881-884 ◽  
Author(s):  
Sheng Zhang ◽  
Jiahong Li ◽  
Luyao Zhang
Keyword(s):  
Exact Solutions ◽  
Function Method ◽  
Evolution Equations ◽  
Mathematical Tool ◽  
Direct Algorithm ◽  
Linear Evolution ◽  
Non Linear ◽  
De Vries ◽  
Linear Evolution Equations

In this paper, a direct algorithm of the exp-function method is proposed for exactly solving non-linear evolution equations. To illustrate the validity and advantages of the algorithm, the Korteweg-de Vries and Jimbo-Miwa equations are considered. As a result, exact solutions are obtained. It is shown that the exp-function method with the direct algorithm provides a simpler but effective mathematical tool for constructing exact solutions of non-linear evolution equations in fluids.

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