Journal of Nonlinear Mathematical Physics

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Volume 27, Issue 3, May 2020, Pages 453 - 477

Hierarchies of q-discrete Painlevé equations

Authors
Huda Alrashdi
School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia,halr6311@uni.sydney.edu.au*
Nalini Joshi
School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia,nalini.joshi@sydney.edu.au
Dinh Thi Tran
School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006, Australia,dinhthi.tran@sydney.edu.au
*

current email: halrashidi@ksu.edu.sa

Received 10 May 2019, Accepted 11 November 2019, Available Online 4 May 2020.
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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<Previous Article In Issue
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 3
Pages
453 - 477
Publication Date
2020/05/04
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1757235How to use a DOI?
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/).

Cite this article

risenwbib
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  -