Volume 23, Issue 3, June 2016, Pages 399 - 422
Explicit solutions for a nonlinear model on the honeycomb and triangular lattices
Authors
V.E. Vekslerchik
Usikov Institute for Radiophysics and Electronics 12, Proskura st., Kharkov, 61085, Ukraine,vekslerchik@yahoo.com
Received 26 February 2016, Accepted 2 June 2016, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2016.1204719How to use a DOI?
- Keywords
- integrable lattice models; honeycomb lattice; triangular lattice; bilinear approach; explicit solutions
- Abstract
We study a simple nonlinear model defined on the honeycomb and triangular lattices. We propose a bilin-earization scheme for the field equations and demonstrate that the resulting system is closely related to the well-studied integrable models, such as the Hirota bilinear difference equation and the Ablowitz-Ladik system. This result is used to derive the two sets of explicit solutions: the N-soliton solutions and ones constructed of the Toeplitz determinants.
- Copyright
- © 2016 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 - V.E. Vekslerchik PY - 2021 DA - 2021/01/06 TI - Explicit solutions for a nonlinear model on the honeycomb and triangular lattices JO - Journal of Nonlinear Mathematical Physics SP - 399 EP - 422 VL - 23 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2016.1204719 DO - 10.1080/14029251.2016.1204719 ID - Vekslerchik2021 ER -