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 | |
| Publication status | Published - 2008 Dec |
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Keywords
- Hyperelliptic integral
- Nonlinear differential equation
- Painlevé equation
- Quasi-painlevé property
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Nonlinear differential equations of second Painlevé type with the quasi-Painlevé property along a rectifiable curve. / Shimomura, Shun.
In: Tohoku Mathematical Journal, Vol. 60, No. 4, 12.2008, p. 581-595.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Nonlinear differential equations of second Painlevé type with the quasi-Painlevé property along a rectifiable curve
AU - Shimomura, Shun
PY - 2008/12
Y1 - 2008/12
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
UR - http://www.scopus.com/inward/record.url?scp=59649107042&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=59649107042&partnerID=8YFLogxK
U2 - 10.2748/tmj/1232376167
DO - 10.2748/tmj/1232376167
M3 - Article
AN - SCOPUS:59649107042
VL - 60
SP - 581
EP - 595
JO - Tohoku Mathematical Journal
JF - Tohoku Mathematical Journal
SN - 0040-8735
IS - 4
ER -