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