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arXiv · 1501.02879

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

Xiang-Ke Chang·Xing-Biao Hu·Guoce Xin
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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 $A_1$ $Q$-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 B\"acklund transformation of the Somos-4 recurrence. The related topics about Somos polynomials are also studied.

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Xiang-Ke Chang, Xing-Biao Hu, Guoce Xin. 2015-01-13. Hankel determinant solutions to several discrete integrable systems and the Laurent Property. https://doi.org/10.1137/130911676

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