Volume 18, Issue 3, September 2011, Pages 443 - 459
Toda–Heisenberg Chain: Interacting σ-Fields in Two Dimensions
Received 28 February 2011, Accepted 28 March 2011, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925111001702How to use a DOI?
- Keywords
- Toda–Heisenberg chain; interacting sigma-fields; relativistic Toda chain; Ruijsenaars–Toda lattice; Ablowitz–Ladik hierarchy; dark-soliton solutions
- Abstract
We study a (2 ± 1)-dimensional system that can be viewed as an infinite number of O(3) σ-fields coupled by a nearest-neighbour Heisenberg-like interaction. We reduce the field equations of this model to an integrable system that is closely related to the two-dimensional relativistic Toda chain and the Ablowitz–Ladik equations. Using this reduction we obtain the dark-soliton solutions of our model.
- Copyright
- © 2011 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 - G. M. Pritula AU - V. E. Vekslerchik PY - 2021 DA - 2021/01/07 TI - Toda–Heisenberg Chain: Interacting σ-Fields in Two Dimensions JO - Journal of Nonlinear Mathematical Physics SP - 443 EP - 459 VL - 18 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001702 DO - 10.1142/S1402925111001702 ID - Pritula2021 ER -