HOME > Table of Contents and Abstracts > Vol. 60, No. 4
Tohoku Mathematical Journal
SECOND SERIES VOL. 60, NO. 4
|Tohoku Math. J.|
60 (2008), 581-595
NONLINEAR DIFFERENTIAL EQUATIONS OF SECOND PAINLEVÉ TYPE WITH THE QUASI-PAINLEVÉ PROPERTY
(Received March 3, 2008, revised June 4, 2008)
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.
2000 Mathematics Subject Classification.
Primary 34M55; Secondary 34M35.
Key words and phrases.
Nonlinear differential equation, quasi-Painlevé property, Painlevé equation, hyperelliptic integral.
To the top of this page
Back to the Contents