Hankel Determinant Solutions to Several Discrete Integrable Systems and the Laurent Property

نویسندگان

  • Xiang-Ke Chang
  • Xing-Biao Hu
  • Guoce Xin
چکیده

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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عنوان ژورنال:
  • SIAM J. Discrete Math.

دوره 29  شماره 

صفحات  -

تاریخ انتشار 2015