Hankel determinant solutions to several discrete integrable systems and the Laurent Property

2015/01/25 by Xiang-Ke Chang, Xing-Biao Hu, Guoce Xin · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.CO #math.MP #nlin.SI #msc:11B83 #msc:37J35 #msc:15B05 #msc:11Y65

paper · pdf · doi:10.1137/130911676

published as SIAM J. Discrete Math. 29(1): 667--682, 2015 · 16 pages

arxiv created 2015/01/25 · arxiv updated 2015/04/13

Abstract

Many discrete integrable systems exhibit the Laurent phenomenon. In this paper, we investigate three integrable systems: the Somos-4 recurrence, the Somos-5 recurrence and a system related to so-called A₁ Q-system, whose general solutions are derived in terms of Hankel determinant. As a result, we directly confirm that they satisfy the Laurent property. Additionally, it is shown that the Somos-5 recurrence can be viewed as a specified Bäcklund transformation of the Somos-4 recurrence. The related topics about Somos polynomials are also studied.

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