Journal of Nonlinear Mathematical Physics

Volume 10, Issue 2, May 2003, Pages 215 - 228

A Unified Description of the Asymmetric q-PV and d-PIV Equations and their Schlesinger Transformations

Authors
B. Grammaticos, A. Ramani, Y. Ohta
Corresponding Author
B. Grammaticos
Received 3 July 2002, Revised 27 September 2002, Accepted 1 October 2002, Available Online 1 May 2003.
DOI
10.2991/jnmp.2003.10.2.5How to use a DOI?
Abstract

We present a geometric description, based on the affine Weyl group E (1) 6 , of two discrete analogues of the Painlevé VI equation, known as the asymmetric q-PV and asymmetric d-PIV. This approach allows us to describe in a unified way the evolution of the mapping along the independent variable and along the various parameters (the latter evolution being the one induced by the Schlesinger transformations). It turns out that both discrete Painlevé equations exhibit the property of self-duality: the same equation governs the evolution along any direction in the space of E (1) 6 .

Copyright
© 2006, 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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
10 - 2
Pages
215 - 228
Publication Date
2003/05/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2003.10.2.5How to use a DOI?
Copyright
© 2006, 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

TY  - JOUR
AU  - B. Grammaticos
AU  - A. Ramani
AU  - Y. Ohta
PY  - 2003
DA  - 2003/05/01
TI  - A Unified Description of the Asymmetric q-PV and d-PIV Equations and their Schlesinger Transformations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 215
EP  - 228
VL  - 10
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2003.10.2.5
DO  - 10.2991/jnmp.2003.10.2.5
ID  - Grammaticos2003
ER  -