On the crystal limit of the q-difference sixth Painlevé equation

2024/08/15 by Nalini Joshi, Joshi, Nalini, Pieter Roffelsen +1 · 1 voice · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Polynomial and algebraic computation #math-ph #nlin.SI

paper · pdf · doi:10.48550/arxiv.2408.07963

openalex publication_date 2024/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Riemann-Hilbert correspondence associated with the q-difference sixth Painlevé equation in the crystal limit, i.e. q→ 0, and show two main results. First, the limit of this generically highly transcendental mapping is shown to exist. Second, we show that the limiting map is bi-rational and describe it explicitly.

Cited by

• On finding formal power-logarithmic expansions of solutions to q-difference equations
• Arithmetic dynamics of a discrete Painlevé equation

Discussions

• Woo hoo 🎉 The paper in which we introduce the “crystal limit” for q-difference Painlevé equations has been accepted in Journal of Nonlinear Science 🎊 👉🏼 arxiv.org/abs/2408.07963 [bsky, 8 points, 1 comments]

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