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Burchnall-Chaundy polynomials and the Laurent phenomenon

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posted on 2015-05-20, 10:27 authored by Alexander VeselovAlexander Veselov, R. Willox
The Burchnall-Chaundy polynomials Pn(z) are determined by the differential recurrence relation with The fact that this recurrence relation has all solutions polynomial is not obvious and is similar to the integrality of Somos sequences and the Laurent phenomenon. We discuss this parallel in more detail and extend it to two difference equations and related to two different KdV-type reductions of the Hirota-Miwa and Dodgson octahedral equations. As a corollary we have a new form of the Burchnall-Chaundy polynomials in terms of the initial data , which is shown to be Laurent.

Funding

APV is grateful to the Graduate School of Mathematical Sciences of the University of Tokyo for the support of his visit in April–July 2014, during which this work was done. RW would like to acknowledge support from the Japan Society for the Promotion of Science, through the JSPS grant: KAKENHI 24540204. The work of APV was partially supported by the EPSRC [grant number EP/J00488X/1].

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Physics A: Mathematical and Theoretical

Volume

48

Issue

20

Pages

1 - 15

Citation

VESELOV, A.P. and WILLOX, R., 2015. Burchnall-Chaundy polynomials and the Laurent phenomenon. Journal of Physics A: Mathematical and Theoretical, 48 (20), 205201.

Publisher

© Institute of Physics Publishing

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2015

Notes

This article was published in the Journal of Physics A: Mathematical and Theoretical [© Institute of Physics Publishing] and the definitive version is available at: http://dx.doi.org/10.1088/1751-8113/48/20/205201

DOI

ISSN

1751-8113

eISSN

1751-8121

Publisher version

Language

  • en

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    Loughborough Publications

    Categories

    Keywords

    Burchnall-Chaundy polynomialsDiscrete integrable systemsLaurent phenomenonMathematical Sciences not elsewhere classified

    Licence

    CC BY-NC-ND 4.0

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