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About several classes of bi-orthogonal polynomials and discrete integrable systems

Xiang-Ke Chang Xiao-Min Chen Xing-Biao Hu Hon-Wah Tam

Dynamical Systems mathscidoc:1912.43166

Journal of Physics A: Mathematical and Theoretical, 48, (1), 015204, 2014.12
By introducing some special bi-orthogonal polynomials, we derive the so-called discrete hungry quotient-difference (dhQD) algorithm and a system related to the QD-type discrete hungry LotkaVolterra (QD-type dhLV) system, together with their Lax pairs. These two known equations can be regarded as extensions of the QD algorithm. When this idea is applied to a higher analogue of the discrete-time Toda (HADT) equation and the quotientquotient-difference (QQD) scheme proposed by Spicer, Nijhoff and van der Kamp, two extended systems are constructed. We call these systems the hungry forms of the higher analogue discrete-time Toda (hHADT) equation and the quotient-quotient-difference (hQQD) scheme, respectively. In addition, the corresponding Lax pairs are provided.
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@inproceedings{xiang-ke2014about,
  title={About several classes of bi-orthogonal polynomials and discrete integrable systems},
  author={Xiang-Ke Chang, Xiao-Min Chen, Xing-Biao Hu, and Hon-Wah Tam},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112706232183726},
  booktitle={Journal of Physics A: Mathematical and Theoretical},
  volume={48},
  number={1},
  pages={015204},
  year={2014},
}
Xiang-Ke Chang, Xiao-Min Chen, Xing-Biao Hu, and Hon-Wah Tam. About several classes of bi-orthogonal polynomials and discrete integrable systems. 2014. Vol. 48. In Journal of Physics A: Mathematical and Theoretical. pp.015204. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112706232183726.
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