Volume 20, Issue 4, December 2013, Pages 565 - 576
Contiguity relations for linearisable systems of Gambier type
Authors
A. Ramani
Centre de Physique Théorique, Ecole Polytechnique CNRS, 91128 Palaiseau, France,Alfred.Ramani@cpht.polytechnique.fr
B. Grammaticos
IMNC, Université Paris VII & XI, CNRS, UMR 8165 Bât. 440, 91406 Orsay, Francegrammaticos@imnc.in2p3.fr
P. Guha*
IHES, 35 route de Chartres 91440 Bures sur Yvette, Francepartha@boson.bose.res.in
*
Permanent address: Satyendranath Nath Bose National Centre for Basic Sciences, JD Block, Sector III, Kolkata - 700098, India.
Received 17 August 2013, Accepted 4 October 2013, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2013.868269How to use a DOI?
- Keywords
- contiguity relations; linearisability; Gambier equation
- Abstract
We introduce the Schlesinger transformations for the Gambier, linearisable, equation and by combining the former construct the contiguity relations of the solutions of the latter. We extend the approach to the discrete domain obtaining thus the Schlesinger transformations and the contiguity relations of the solutions of the Gambier mapping. In all cases the resulting contiguity relation is a linearisable equation, involving free functions, and which can be related to the generic Gambier mapping.
- Copyright
- © 2013 The Authors. Published by Atlantis Press 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
TY - JOUR AU - A. Ramani AU - B. Grammaticos AU - P. Guha PY - 2021 DA - 2021/01/06 TI - Contiguity relations for linearisable systems of Gambier type JO - Journal of Nonlinear Mathematical Physics SP - 565 EP - 576 VL - 20 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.868269 DO - 10.1080/14029251.2013.868269 ID - Ramani2021 ER -