Journal of Nonlinear Mathematical Physics

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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
23 - 3
Pages
368 - 382
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2016.1199498How to use a DOI?
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  -