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On a General Singular Solution of the Fifth Painlevé Equation Along the Positive Real Axis

On a General Singular Solution of the Fifth Painlevé Equation Along the Positive Real Axis We propose a system of non-linear equations equivalent to the fifth Painlevé equation, which enables us to examine the general singular solution given by Andreev and Kitaev along the positive real axis. We present a two-parameter family of asymptotic solutions corresponding to this general singular solution, and pose a conjecture. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

On a General Singular Solution of the Fifth Painlevé Equation Along the Positive Real Axis

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-021-00391-8
Publisher site
See Article on Publisher Site

Abstract

We propose a system of non-linear equations equivalent to the fifth Painlevé equation, which enables us to examine the general singular solution given by Andreev and Kitaev along the positive real axis. We present a two-parameter family of asymptotic solutions corresponding to this general singular solution, and pose a conjecture.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Dec 1, 2021

Keywords: Fifth Painlevé equation; General singular solution; Isomonodromy deformation; Asymptotic expansion; 34M55; 33E17; 34M25; 34M30

References