On the Exact Gevrey Order of Formal Puiseux Series Solutions to the Third Painlevé Equation

2019 ◽  
Vol 25 (4) ◽  
pp. 681-690
Author(s):  
A. Parusnikova ◽  
A. Vasilyev
Keyword(s):  
Painlevé Equation ◽  
Series Solutions ◽  
Puiseux Series ◽  
The Third ◽  
Gevrey Order ◽  
Painleve Equation

Solution of the equivalence problem for the third Painlevé equation

2015 ◽  
Vol 56 (1) ◽  
pp. 013507 ◽  
Author(s):  
Yulia Yu. Bagderina ◽  
Nikolai N. Tarkhanov
Keyword(s):  
Equivalence Problem ◽  
Painlevé Equation ◽  
The Third ◽  
Painleve Equation

Asymptotic forms of solutions to the third Painlevé equation

2008 ◽  
Vol 78 (2) ◽  
pp. 765-768 ◽  
Author(s):  
A. D. Bruno ◽  
I. V. Goryuchkina
Keyword(s):  
Painlevé Equation ◽  
The Third ◽  
Painleve Equation ◽  
Asymptotic Forms

scholarly journals Solutions of the third Painlevé equation I

1998 ◽  
Vol 151 ◽  
pp. 1-24 ◽  
Author(s):  
Hiroshi Umemura ◽  
Humihiko Watanabe
Keyword(s):  
Painlevé Equation ◽  
Classical Solutions ◽  
The Third ◽  
Painleve Equation ◽  
Algebraic Solutions

Abstract.We classify transcendental classical solutions of the third Painlevé equation. This result combined with the list of algebraic solutions in [11] gives a complete table of classical solutions of the third Painlevé equation.

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