The Padé interpolation method applied to additive difference Painlevé equations

2017/06/30 by Hidehito Nagao, Nagao, Hidehito
Computer Science · Mathematics · Physics and Astronomy · #33D15 #34M55 #39A10 #41A05 #41A21 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1706.10101

openalex publication_date 2017/06/30 · openalex created_date 2022/11/14 · openalex updated_date 2026/07/28

Abstract

We study Padé interpolation problems on an additive grid, related to additive difference (d-) Painlevé equations of type E₇⁽¹⁾, E₆⁽¹⁾, D₄⁽¹⁾ and A₃⁽¹⁾. By choosing suitable Padé problems, we can derive time evolution equations, scalar Lax pairs of contiguous type and determinant formulae of special solutions given in terms of hypergeometric functions, for the corresponding d-Painlevé equations.

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