Discrete Power Functions on a Hexagonal Lattice I: Derivation of defining equations from the symmetry of the Garnier System in two variables

2019/08/27 by Nalini Joshi, Joshi, Nalini, Kenji Kajiwara +5 · 1 citation
Mathematics · Physics and Astronomy · #14H70 #33E17 #34M55 #39A14 #Advanced Combinatorial Mathematics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Photonic Crystals and Applications #msc:14H70 #msc:33E17 #msc:34M55 #msc:39A14 #nlin.SI

paper · pdf · doi:10.48550/arxiv.1908.10060

22 pages

openalex publication_date 2019/08/27 · openalex created_date 2020/10/29 · arxiv created 2021/06/10 · arxiv updated 2021/06/11 · openalex updated_date 2026/07/28

Abstract

The discrete power function on the hexagonal lattice proposed by Bobenko et al is considered, whose defining equations consist of three cross-ratio equations and a similarity constraint. We show that the defining equations are derived from the discrete symmetry of the Garnier system in two variables.

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• Special solutions to five autonomous integrable partial difference equations via the third and sixth Painlevé equations and the Garnier system in two variables

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