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Title: Burchnall-Chaundy polynomials and the Laurent phenomenon
Authors: Veselov, A.P.
Willox, R.
Keywords: Burchnall-Chaundy polynomials
Discrete integrable systems
Laurent phenomenon
Issue Date: 2015
Publisher: © Institute of Physics Publishing
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.
Abstract: The Burchnall-Chaundy polynomials P<inf>n</inf>(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.
Description: 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
Sponsor: 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].
Version: Accepted for publication
DOI: 10.1088/1751-8113/48/20/205201
URI: https://dspace.lboro.ac.uk/2134/17543
Publisher Link: http://dx.doi.org/10.1088/1751-8113/48/20/205201
ISSN: 1751-8113
Appears in Collections:Published Articles (Maths)

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