Journal of Nonlinear Mathematical Physics

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, France grammaticos@imnc.in2p3.fr
P. Guha*
IHES, 35 route de Chartres 91440 Bures sur Yvette, France partha@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
https://doi.org/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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
20 - 4
Pages
565 - 576
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2013.868269How to use a DOI?
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
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  - https://doi.org/10.1080/14029251.2013.868269
ID  - Ramani2021
ER  -