Bäcklund transformations and Painlevé analysis: Exact soliton solutions for strongly rarefied relativistic cold plasma

1997 ◽  
Vol 4 (11) ◽  
pp. 3910-3922 ◽  
Author(s):  
A. H. Khater ◽  
D. K. Callebaut ◽  
A. B. Shamardan ◽  
R. S. Ibrahim
Keyword(s):  
Cold Plasma ◽  
Soliton Solutions ◽  
Bäcklund Transformations ◽  
Painlevé Analysis ◽  
Backlund Transformations ◽  
Painleve Analysis ◽  
Exact Soliton Solutions

scholarly journals Bäcklund Transformation and New Exact Solutions of the Sharma-Tasso-Olver Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Lin Jianming ◽  
Ding Jie ◽  
Yuan Wenjun
Keyword(s):  
Exact Solutions ◽  
Bäcklund Transformation ◽  
Analytic Study ◽  
Bäcklund Transformations ◽  
Painlevé Analysis ◽  
Backlund Transformation ◽  
New Exact Solutions ◽  
Backlund Transformations ◽  
Painleve Analysis

The Sharma-Tasso-Olver (STO) equation is investigated. The Painlevé analysis is efficiently used for analytic study of this equation. The Bäcklund transformations and some new exact solutions are formally derived.

INTEGRABLE ASPECTS OF NONCOMMUTATIVE ANTI-SELF-DUAL YANG-MILLS EQUATIONS

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2237-2238 ◽  
Author(s):  
MASASHI HAMANAKA
Keyword(s):  
Integrable Systems ◽  
Soliton Solutions ◽  
Bäcklund Transformations ◽  
Soliton Theory ◽  
Yang Mills ◽  
Backlund Transformations ◽  
Exact Soliton Solutions

We discuss extension of soliton theory and integrable systems to non-commutative (NC) spaces, focusing on integrable aspects of NC Anti-Self-Dual Yang-Mills (ASDYM) equations. We give exact soliton solutions (with both finite- and infinite-action solutions) by means of Bäcklund transformations. In the construction of NC soliton solutions, one kind of NC determinants, quasideterminants, play crucial roles. This is partially based on collaboration with C. R. Gilson and J. J. C. Nimmo (Glasgow).

scholarly journals Painleve Test and Discrete Boltzmann Equations

1989 ◽  
Vol 42 (1) ◽  
pp. 1 ◽  
Author(s):  
N Euler ◽  
W-H Steeb
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Vector Fields ◽  
Lie Symmetry ◽  
Bäcklund Transformations ◽  
Painlevé Analysis ◽  
Painlevé Test ◽  
Boltzmann Equations ◽  
Backlund Transformations ◽  
Painleve Analysis

The Painleve test for various discrete Boltzmann equations is performed. The connection with integrability is discussed. Furthermore the Lie symmetry vector fields are derived and group-theoretical reduction of the discrete Boltzmann equations to ordinary differentiable equations is performed. Lie Backlund transformations are gained by performing the Painleve analysis for the ordinary differential equations

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