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

Xiang-Ke Chang Xing-Biao Hu Guoce Xin

Dynamical Systems mathscidoc:1912.43169

SIAM Journal on Discrete Mathematics, 29, (1), 667-682, 2015.3
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 A_1-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 Backlund transformation of the Somos-4 recurrence. Related topics about Somos polynomials are also studied.
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@inproceedings{xiang-ke2015hankel,
  title={Hankel determinant solutions to several discrete integrable systems and the Laurent property},
  author={Xiang-Ke Chang, Xing-Biao Hu, and Guoce Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112715074058729},
  booktitle={SIAM Journal on Discrete Mathematics},
  volume={29},
  number={1},
  pages={667-682},
  year={2015},
}
Xiang-Ke Chang, Xing-Biao Hu, and Guoce Xin. Hankel determinant solutions to several discrete integrable systems and the Laurent property. 2015. Vol. 29. In SIAM Journal on Discrete Mathematics. pp.667-682. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112715074058729.
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