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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:1412.3541 (nlin)
[Submitted on 11 Dec 2014 (v1), last revised 26 Nov 2015 (this version, v2)]

Title:Asymptotic behaviour of the fourth Painlevé transcendents in the space of initial values

Authors:Nalini Joshi, Milena Radnović
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Abstract:We study the asymptotic behaviour of solutions of the fourth Pain\-levé equation as the independent variable goes to infinity in its space of (complex) initial values, which is a generalisation of phase space described by Okamoto. We show that the limit set of each solution is compact and connected and, moreover, that any non-special solution has an infinite number of poles and infinite number of zeroes.
Comments: 30 pages, 1 figure; Added Section 3 on the special solutions
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Classical Analysis and ODEs (math.CA)
MSC classes: 34M55, 34M30
Cite as: arXiv:1412.3541 [nlin.SI]
  (or arXiv:1412.3541v2 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.1412.3541

Submission history

From: Milena Radnovic [view email]
[v1] Thu, 11 Dec 2014 05:13:41 UTC (28 KB)
[v2] Thu, 26 Nov 2015 05:58:52 UTC (28 KB)
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