A class of differential equations of PI-type with the quasi-Painlevé property

Shun Shimomura

doi:10.1007/s10231-006-0004-3

A class of differential equations of PI-type with the quasi-Painlevé property

Shun Shimomura

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

We present a certain class of second order nonlinear differential equations containing the first Painlevé equation (PI). Each equation in it admits the quasi-Painlevé property, namely every movable singularity of a general solution is at most an algebraic branch point. For these equations we show some basic properties.

Original language	English
Pages (from-to)	267-280
Number of pages	14
Journal	Annali di Matematica Pura ed Applicata
Volume	186
Issue number	2
DOIs	https://doi.org/10.1007/s10231-006-0004-3
Publication status	Published - 2007 Apr
Externally published	Yes

Keywords

Hyperelliptic integral
Nonlinear differential equation
Painlevé equation
Quasi-Painlevé property

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s10231-006-0004-3

Cite this

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title = "A class of differential equations of PI-type with the quasi-Painlev{\'e} property",

abstract = "We present a certain class of second order nonlinear differential equations containing the first Painlev{\'e} equation (PI). Each equation in it admits the quasi-Painlev{\'e} property, namely every movable singularity of a general solution is at most an algebraic branch point. For these equations we show some basic properties.",

keywords = "Hyperelliptic integral, Nonlinear differential equation, Painlev{\'e} equation, Quasi-Painlev{\'e} property",

author = "Shun Shimomura",

year = "2007",

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doi = "10.1007/s10231-006-0004-3",

language = "English",

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AB - We present a certain class of second order nonlinear differential equations containing the first Painlevé equation (PI). Each equation in it admits the quasi-Painlevé property, namely every movable singularity of a general solution is at most an algebraic branch point. For these equations we show some basic properties.

KW - Hyperelliptic integral

KW - Nonlinear differential equation

KW - Painlevé equation

KW - Quasi-Painlevé property

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JF - Annali di Matematica Pura ed Applicata

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ER -

A class of differential equations of PI-type with the quasi-Painlevé property

Abstract

Keywords

ASJC Scopus subject areas

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