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

Xiang Ke Chang, Xiao Min Chen, Xing Biao Hu, Hon Wah TAM

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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.

Original languageEnglish
Article number015204
JournalJournal of Physics A: Mathematical and Theoretical
Volume48
Issue number1
DOIs
Publication statusPublished - 9 Jan 2015

Scopus Subject Areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

User-Defined Keywords

  • discrete integrable systems
  • Lax pair
  • orthogonal polynomials

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