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.
Citation
Shun Shimomura. "Nonlinear differential equations of second Painlevé type with the quasi-Painlevé property." Tohoku Math. J. (2) 60 (4) 581 - 595, 2008. https://doi.org/10.2748/tmj/1232376167
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