Backlund transformations and Painleve analysis: exact solutions for a Grad-Shafranov-type magnetohydrodynamic equilibrium

1997 ◽  
Vol 58 (1) ◽  
pp. 51-69 ◽  
Author(s):  
A. Kater
Keyword(s):  
Exact Solutions ◽  
Bäcklund Transformations ◽  
Painlevé Analysis ◽  
Backlund Transformations ◽  
Painleve Analysis

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.

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

scholarly journals Painlevé analysis and exact solutions of bosonized N = 1 supersymmetric Burgers equation

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Bo Ren
Keyword(s):  
Exact Solutions ◽  
Burgers Equation ◽  
Expansion Method ◽  
Singularity Analysis ◽  
Bäcklund Transformations ◽  
Painlevé Analysis ◽  
Explicit Solutions ◽  
Bosonic System ◽  
Painlevé Property ◽  
Backlund Transformations

AbstractBased on the bosonization approach, the N = 1 supersymmetric Burgers (SB) system is transformed to a coupled pure bosonic system. The Painlevé property and the Bäcklund transformations (BT) of the bosonized SB (BSB) system are obtained through standard singularity analysis. Explicit solutions such as the muti-solitarywaves and error functionwaves are provided for the BT. The exact solutions of the BSB system are obtained from the generalized tanh expansion method.

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