Hierarchies of q-discrete Painlevé equations
current email: halrashidi@ksu.edu.sa
- DOI
- 10.1080/14029251.2020.1757235How to use a DOI?
- Keywords
- q-discrete Painlevé equations; Lax pair; Hierarchies; Bäcklund transformations
- Abstract
In this paper, we construct a new hierarchy based on the third q-discrete Painlevé equation (qPIII) and also study the hierarchy of the second q-discrete Painlevé equation (qPII). Both hierarchies are derived by using reductions of the general lattice modified Korteweg-de Vries equation. Our results include Lax pairs for both hierarchies and these turn out to be higher degree expansions of the non-resonant ones found by Joshi and Nakazono [29] for the second-order cases. We also obtain Bäcklund transformations for these hierarchies. Special q-rational solutions of the hierarchies are constructed and corresponding q-gamma functions that solve the associated linear problems are derived.
- Copyright
- © 2020 The Authors. Published by Atlantis and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
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TY - JOUR AU - Huda Alrashdi AU - Nalini Joshi AU - Dinh Thi Tran PY - 2020 DA - 2020/05/04 TI - Hierarchies of q-discrete Painlevé equations JO - Journal of Nonlinear Mathematical Physics SP - 453 EP - 477 VL - 27 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2020.1757235 DO - 10.1080/14029251.2020.1757235 ID - Alrashdi2020 ER -