About several classes of bi-orthogonal polynomials and discrete integrable systems
Abstract
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 Lotka-Volterra (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 quotient-quotient-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.
Keywords
Cite
@article{arxiv.1411.4220,
title = {About several classes of bi-orthogonal polynomials and discrete integrable systems},
author = {Xiangke Chang and Xiaomin Chen and Xingbiao Hu and Honwah Tam},
journal= {arXiv preprint arXiv:1411.4220},
year = {2015}
}
Comments
19 pages