Journal of Nonlinear Mathematical Physics

Volume 27, Issue 4, September 2020, Pages 688 - 696

Gambier lattices and other linearisable systems

Authors
Basil Grammaticos*, Alfred Ramani
IMNC, CNRS, Université Paris-Diderot, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
*Corresponding author’s email address: grammati@paris7.jussieu.fr
Corresponding Author
Basil Grammaticos
Received 4 November 2019, Accepted 29 February 2020, Available Online 4 September 2020.
DOI
10.1080/14029251.2020.1819620How to use a DOI?
Keywords
integrable lattices; Gambier mapping; singularity confinement; growth properties
Abstract

We propose two different appraoches to extending the Gambier mapping to a two-dimensional lattice equation. A first approach relies on a hypothesis of separate evolutions in each of the two directions. We show that known equations like the Startsev-Garifullin-Yamilov equation, the Hietarinta equation, as well as one proposed by the current authors, are in fact Gambier lattices. A second approach, based on the same principle as the Gambier equation, that of two linearisable equations in cascade, constructs a Gambier lattice in the form of a system of two coupled Burgers equations. The (slow) growth properties of the latter are in agreement with its linearisable character.

Copyright
© 2020 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
27 - 4
Pages
688 - 696
Publication Date
2020/09/04
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1819620How to use a DOI?
Copyright
© 2020 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  - Basil Grammaticos
AU  - Alfred Ramani
PY  - 2020
DA  - 2020/09/04
TI  - Gambier lattices and other linearisable systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 688
EP  - 696
VL  - 27
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1819620
DO  - 10.1080/14029251.2020.1819620
ID  - Grammaticos2020
ER  -