Nonlinear differential equations of second Painlevé type with the quasi-Painlevé property along a rectifiable curve

Shun Shimomura

doi:10.2748/tmj/1232376167

Nonlinear differential equations of second Painlevé type with the quasi-Painlevé property along a rectifiable curve

Shun Shimomura

Department of Mathematics

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

3 Citations (Scopus)

Abstract

We present a class of nonlinear differential equations of second Painlevé type. These equations, with a single exception, admit the quasi-Painlevé property along a rectifiable curve, that is, for general solutions, every movable singularity defined by a rectifiable curve is at most an algebraic branch point. Moreover we discuss the global many-valuedness of their solutions. For the exceptional equation, by the method of successive approximation, we construct a general solution having a movable logarithmic branch point.

Original language	English
Pages (from-to)	581-595
Number of pages	15
Journal	Tohoku Mathematical Journal
Volume	60
Issue number	4
DOIs	https://doi.org/10.2748/tmj/1232376167
Publication status	Published - 2008 Dec

Keywords

Hyperelliptic integral
Nonlinear differential equation
Painlevé equation
Quasi-painlevé property

ASJC Scopus subject areas

Mathematics(all)

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title = "Nonlinear differential equations of second Painlev{\'e} type with the quasi-Painlev{\'e} property along a rectifiable curve",

abstract = "We present a class of nonlinear differential equations of second Painlev{\'e} type. These equations, with a single exception, admit the quasi-Painlev{\'e} property along a rectifiable curve, that is, for general solutions, every movable singularity defined by a rectifiable curve is at most an algebraic branch point. Moreover we discuss the global many-valuedness of their solutions. For the exceptional equation, by the method of successive approximation, we construct a general solution having a movable logarithmic branch point.",

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

author = "Shun Shimomura",

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language = "English",

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AU - Shimomura, Shun

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N2 - We present a class of nonlinear differential equations of second Painlevé type. These equations, with a single exception, admit the quasi-Painlevé property along a rectifiable curve, that is, for general solutions, every movable singularity defined by a rectifiable curve is at most an algebraic branch point. Moreover we discuss the global many-valuedness of their solutions. For the exceptional equation, by the method of successive approximation, we construct a general solution having a movable logarithmic branch point.

AB - We present a class of nonlinear differential equations of second Painlevé type. These equations, with a single exception, admit the quasi-Painlevé property along a rectifiable curve, that is, for general solutions, every movable singularity defined by a rectifiable curve is at most an algebraic branch point. Moreover we discuss the global many-valuedness of their solutions. For the exceptional equation, by the method of successive approximation, we construct a general solution having a movable logarithmic branch point.

KW - Hyperelliptic integral

KW - Nonlinear differential equation

KW - Painlevé equation

KW - Quasi-painlevé property

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