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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:nlin/0310050 (nlin)
[Submitted on 31 Oct 2003]

Title:A unified description of the asymmetric q-P_{v} and d-P_{iv} equations and their Schlesinger transformations

Authors:B. Grammaticos, A. Ramani, Y. Ohta
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Abstract: We present a geometric description, based on the affine Weyl group E_{6}^{(1)}, of two discrete analogues of the Painlevé VI equation, known as the asymmetric q-P_{V} and asymmetric d-P_{IV}. 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_{6}^{(1)}.
Comments: Published by JNMP at this http URL
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:nlin/0310050 [nlin.SI]
  (or arXiv:nlin/0310050v1 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.nlin/0310050
Journal reference: J. Nonlinear Math. Phys., volume 10, no. 2 (2003) 215-228
Related DOI: https://doi.org/10.2991/jnmp.2003.10.2.5

Submission history

From: Basile Grammaticos [view email] [via BOLINA proxy]
[v1] Fri, 31 Oct 2003 17:19:58 UTC (15 KB)
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