Asymptotic behaviour of the third Painlevé transcendents in the space of initial values

2018/01/22 by Nalini Joshi, Joshi, Nalini, Milena Radnović +1
Mathematics · Physics and Astronomy · #34M30 #34M55 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Meromorphic and Entire Functions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1801.07596

openalex publication_date 2018/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behaviour of the solutions of the generic (D₆⁽¹⁾-type) third Painlevé equation in the space of initial values as the independent variable approaches infinity (or zero) and show that the limit set of each solution is compact and connected. Moreover, we prove that any solution with essential singularity at infinity has an infinite number of poles and zeroes, and similarly at the origin.

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