scholarly journals Differential Galois Theory and Isomonodromic Deformations

2019 ◽  
Author(s):  
David Blázquez Sanz ◽  
◽  
Guy Casale ◽  
Juan Sebastián Díaz Arboleda ◽  
◽  
...  
Keyword(s):  
Galois Theory ◽  
Differential Galois Theory ◽  
Isomonodromic Deformations

scholarly journals Differential Galois Theory and Lie Symmetries

2015 ◽  
Author(s):  
David Blázquez-Sanz ◽  
◽  
Juan J. Morales-Ruiz ◽  
Jacques-Arthur Weil ◽  
◽  
...  
Keyword(s):  
Galois Theory ◽  
Lie Symmetries ◽  
Differential Galois Theory

scholarly journals Rational KdV Potentials and Differential Galois Theory

2019 ◽  
Author(s):  
Sonia Jiménez ◽  
◽  
Juan J. Morales-Ruiz ◽  
Raquel Sánchez-Cauce ◽  
María-Ángeles Zurro ◽  
...  
Keyword(s):  
Galois Theory ◽  
Differential Galois Theory

scholarly journals Second proof of the irreducibility of the first differential equation of painlevé

1990 ◽  
Vol 117 ◽  
pp. 125-171 ◽  
Author(s):  
Hiroshi Umemura
Keyword(s):  
Differential Equation ◽  
General Theory ◽  
Galois Theory ◽  
Rigorous Proof ◽  
Mathematical Foundation ◽  
Differential Galois Theory ◽  
Infinite Dimensional ◽  
Finite Dimensional

In our paper [U2], we proved the irreducibility of the first differential equation y″ = 6y2 + x of Painlevé. In that paper we explained the origin of the problem and the importance of giving a rigorous proof. We can say that our method in [U2] is algebraic and finite dimensional in contrast to a prediction of Painlevé who expected a proof depending on the infinite dimensional differential Galois theory. Even nowadays the latter remains to be established. It seems that Painlevé needed an armament with the general theory (the infinite dimensional differential Galois theory) in the controversy with R. Liouville on the mathematical foundation of the proof of the irreducibility of the first differential equation (1902-03).

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