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Andrei Prokhorov

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Articles by Andrei Prokhorov

Asymptotic Properties of Special Function Solutions of the Painlevé III Equation for Fixed Parameters

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By Hao Pan, Andrei Prokhorov
| Wiley Online Library Verified
1 Introduction Painlevé equations are six nonlinear second-order ordinary differential equations. They are written in the form of u ′ ′ = R ( u ′ , u , t ) $u^{\prime \prime }=R(u^{\prime },u,t)$ with R $R$ a rational function. Their solutions have the so-called Painlevé property. This means that the locations of singularities of branching type in the complex plane do not depend on the initial conditions, but the locations of isolated singularities might depend on the initial conditions.
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[2407.04852] Small $x$ asymptotics for special function solutions of Painlevé III equation

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By Andrei Prokhorov
| arXiv
arXiv:2407.04852 (math) View PDF HTML (experimental) Comments: Subjects: Classical Analysis and ODEs (math.CA); Mathematical Physics (math-ph); Complex Variables (math.CV); Exactly Solvable and Integrable Systems (nlin.SI) MSC classes: 33C10, 33E17, 34E05, 34M55, 34M56 Cite as: arXiv:2407.04852 [math.CA] (or arXiv:2407.04852v1 [math.CA] for this version) Submission history From: Andrei Prokhorov [ view email] [v1] Fri, 5 Jul 2024 20:21:02 UTC (343 KB) Bibliographic Tools Bibliographic...
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