The power expansions of the solutions of the first painlevé hierarchy

The power expansions of the solutions of the first painlevé hierarchy

In this paper we consider a hierarchy of the first Painlevé equation's higher order analogues. For these equations three types of power expansions, i.e. holomorphic, polar and asymptotic are found. As an example the equation of the fourth order is considered. First Published Online: 14 Oct...

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Bibliographic Details
Main Authors: A. A. Grigor'ev, V. I. Gromak
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2006-12-01
Series:Mathematical Modelling and Analysis
Subjects:
Painlevé equation
P‐type equations
power expansions
power geometry
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/9648
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spelling doaj-b99ee9fe65b145f0ac4f9220a326e2852021-07-02T08:03:55ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102006-12-0111410.3846/13926292.2006.9637326The power expansions of the solutions of the first painlevé hierarchyA. A. Grigor'ev0V. I. Gromak1Belarus State University , Nezavisimosti ave.4, Minsk, 220050, BelarusBelarus State University , Nezavisimosti ave.4, Minsk, 220050, Belarus In this paper we consider a hierarchy of the first Painlevé equation's higher order analogues. For these equations three types of power expansions, i.e. holomorphic, polar and asymptotic are found. As an example the equation of the fourth order is considered. First Published Online: 14 Oct 2010 https://journals.vgtu.lt/index.php/MMA/article/view/9648Painlevé equationP‐type equationspower expansionspower geometry
collection DOAJ
language English
format Article
sources DOAJ
author A. A. Grigor'ev
V. I. Gromak
spellingShingle A. A. Grigor'ev
V. I. Gromak
The power expansions of the solutions of the first painlevé hierarchy
Mathematical Modelling and Analysis
Painlevé equation
P‐type equations
power expansions
power geometry
author_facet A. A. Grigor'ev
V. I. Gromak
author_sort A. A. Grigor'ev
title The power expansions of the solutions of the first painlevé hierarchy
title_short The power expansions of the solutions of the first painlevé hierarchy
title_full The power expansions of the solutions of the first painlevé hierarchy
title_fullStr The power expansions of the solutions of the first painlevé hierarchy
title_full_unstemmed The power expansions of the solutions of the first painlevé hierarchy
title_sort power expansions of the solutions of the first painlevé hierarchy
publisher Vilnius Gediminas Technical University
series Mathematical Modelling and Analysis
issn 1392-6292
1648-3510
publishDate 2006-12-01
description In this paper we consider a hierarchy of the first Painlevé equation's higher order analogues. For these equations three types of power expansions, i.e. holomorphic, polar and asymptotic are found. As an example the equation of the fourth order is considered. First Published Online: 14 Oct 2010
topic Painlevé equation
P‐type equations
power expansions
power geometry
url https://journals.vgtu.lt/index.php/MMA/article/view/9648
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AT aagrigorev powerexpansionsofthesolutionsofthefirstpainlevehierarchy
AT vigromak powerexpansionsofthesolutionsofthefirstpainlevehierarchy
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