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/).
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 -