Gambier lattices and other linearisable systems
- 10.1080/14029251.2020.1819620How to use a DOI?
- integrable lattices; Gambier mapping; singularity confinement; growth properties
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.
- © 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 -