Advanced Studies in Pure Mathematics

On elliptic Lax pairs and isomonodromic deformation systems for elliptic lattice equations

Frank Nijhoff and Neslihan Delice

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Abstract

In a previous article [11] a novel class of elliptic Lax pairs for integrable lattice equations was introduced. The present article proposes a de-autonomisation of those Lax pairs leading to a class of elliptic discrete isomonodromic deformation problems. We analyse the systems of compatibility conditions using some (possibly novel) higher order elliptic identities.

Article information

Source
Representation Theory, Special Functions and Painlevé Equations — RIMS 2015, H. Konno, H. Sakai, J. Shiraishi, T. Suzuki and Y. Yamada, eds. (Tokyo: Mathematical Society of Japan, 2018), 487-525

Dates
Received: 4 April 2016
First available in Project Euclid: 21 September 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1537499435

Digital Object Identifier
doi:10.2969/aspm/07610487

Mathematical Reviews number (MathSciNet)
MR3837931

Zentralblatt MATH identifier
07039312

Subjects
Primary: 33E05: Elliptic functions and integrals 33E17: Painlevé-type functions 39A12: Discrete version of topics in analysis 39A14: Partial difference equations

Keywords
Difference equations Lax pair Isomonodromic deformation problems elliptic functions

Citation

Nijhoff, Frank; Delice, Neslihan. On elliptic Lax pairs and isomonodromic deformation systems for elliptic lattice equations. Representation Theory, Special Functions and Painlevé Equations — RIMS 2015, 487--525, Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/aspm/07610487. https://projecteuclid.org/euclid.aspm/1537499435


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