Journal of Nonlinear Mathematical Physics

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Volume 15, Issue 4, December 2008, Pages 353 - 364

Contiguity relations for discrete and ultradiscrete Painleve equations

Authors
A. Ramani, B. Grammaticos, R. Willox
Corresponding Author
A. Ramani
Received 19 May 2008, Accepted 21 August 2008, Available Online 1 December 2008.
DOI
10.2991/jnmp.2008.15.4.1How to use a DOI?
Abstract

We show that the solutions of ultradiscrete Painleve equations satisfy contiguity relations just as their continuous and discrete counterparts. Our starting point are the relations for q-discrete Painleve equations which we then proceed to ultradiscretise. In this paper we obtain results for the one-parameter q-PIII, the symmetric q-PIV and the q-PVI. These results show that there exists a perfect parallel between the properties of continuous, discrete and ultradiscrete Painleve equations.

Copyright
© 2009, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
15 - 4
Pages
353 - 364
Publication Date
2008/12/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2008.15.4.1How to use a DOI?
Copyright
© 2009, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

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TY  - JOUR
AU  - A. Ramani
AU  - B. Grammaticos
AU  - R. Willox
PY  - 2008
DA  - 2008/12/01
TI  - Contiguity relations for discrete and ultradiscrete Painleve equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 353
EP  - 364
VL  - 15
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.4.1
DO  - 10.2991/jnmp.2008.15.4.1
ID  - Ramani2008
ER  -