Sinh-Gordon equation, Painlevé property and Bäcklund transformation

1985 ◽  
Vol 132 (2-3) ◽  
pp. 557-568 ◽  
Author(s):  
A. Grauel
Keyword(s):  
Gordon Equation ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Painlevé Property

scholarly journals The Lattice Sine-Gordon Equation as a Superposition Formula for an NLS-Type System

2021 ◽  
Author(s):  
Dmitry K. Demskoi ◽  
Keyword(s):  
Gordon Equation ◽  
Bäcklund Transformation ◽  
Type System ◽  
Backlund Transformation ◽  
Sine Gordon Equation ◽  
Compatible System

We treat the lattice sine-Gordon equation and two of its generalised symmetries as a compatible system. Elimination of shifts from the two symmetries of the lattice sine-Gordon equation yields an integrable NLS-type system. An auto-Bäcklund transformation and a superposition formula for the NLS-type system is obtained by elimination of shifts from the lattice sine-Gordon equation and its down-shifted version. We use the obtained formulae to calculate a superposition of two and three elementary solutions.

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.

Liouville Equation, Painlevé Property and Bäcklund Transformation

1983 ◽  
Vol 38 (10) ◽  
pp. 1054-1055 ◽  
Author(s):  
W.-H. Steeb ◽  
M. Kloke ◽  
B. M. Spieker
Keyword(s):  
Liouville Equation ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Straightforward Manner ◽  
Painlevé Property

Abstract We demonstrate that a Bäcklund transformation for the Liouville equation can be obtained in a straightforward manner from the Painlevé property of this equation.

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