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Three semi-discrete integrable systems related to orthogonal polynomials and their generalized determinant solutions

Xiao-Min Chen Xiang-Ke Chang Jian-Qing Sun Xing-Biao Hu Yeong-Nan Yeh

Dynamical Systems mathscidoc:1912.43175

Nonlinearity, 28, (7), 2279, 2015.6
In this paper, we present a generalized Toeplitz determinant solution for the generalized Schur flow and propose a mixed form of the two known relativistic Toda chains together with its generalized Toeplitz determinant solution. In addition, we also give a Hankel type determinant solution for a nonisospectral Toda lattice. All these results are obtained by technical determinant operations. As a bonus, we finally obtain some new combinatorial numbers based on the moment relations with respect to these semi-discrete integrable systems and give the corresponding combinatorial interpretations by means of the lattice paths.
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@inproceedings{xiao-min2015three,
  title={Three semi-discrete integrable systems related to orthogonal polynomials and their generalized determinant solutions},
  author={Xiao-Min Chen, Xiang-Ke Chang, Jian-Qing Sun, Xing-Biao Hu, and Yeong-Nan Yeh},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112735524002735},
  booktitle={Nonlinearity},
  volume={28},
  number={7},
  pages={2279},
  year={2015},
}
Xiao-Min Chen, Xiang-Ke Chang, Jian-Qing Sun, Xing-Biao Hu, and Yeong-Nan Yeh. Three semi-discrete integrable systems related to orthogonal polynomials and their generalized determinant solutions. 2015. Vol. 28. In Nonlinearity. pp.2279. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112735524002735.
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