Volume 23, Issue 3, June 2016, Pages 368 - 382
Bi-Hamiltonian structure of the extended noncommutative Toda hierarchy
Authors
Chuanzhong Li
Department of Mathematics, Ningbo University Ningbo, 315211, Zhejiang, P. R. China, Email:lichuanzhong@nbu.edu.cn.
Tao Song
Department of Mathematics, Ningbo University Ningbo, 315211, Zhejiang, P. R. China
Received 23 January 2016, Accepted 8 May 2016, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2016.1199498How to use a DOI?
- Keywords
- noncommutative Toda hierarchy; extended noncommutative Toda hierarchy; bi-Hamiltonian structure
- Abstract
The noncommutative Toda hierarchy is studied with the help of Moyal deformation by a reduction on the non-commutative two dimensional Toda hierarchy. Further we generalize the noncommutative Toda hierarchy to the extended noncommutative Toda hierarchy. To survey on its integrability, we construct the bi-Hamiltonian structure and noncommutative conserved densities of the extended noncommutative Toda hierarchy by means of the R-matrix formalism. This extended noncommutative Toda hierarchy can be reduced to the extended multicomponent Toda hierarchy, extended ZN -Toda hierarchy, extended Toda hierarchy respectively by reductions on Lie algebras.
- 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 - Chuanzhong Li AU - Tao Song PY - 2021 DA - 2021/01/06 TI - Bi-Hamiltonian structure of the extended noncommutative Toda hierarchy JO - Journal of Nonlinear Mathematical Physics SP - 368 EP - 382 VL - 23 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2016.1199498 DO - 10.1080/14029251.2016.1199498 ID - Li2021 ER -