Volume 24, Issue 3, June 2017, Pages 315 - 327
Hamiltonian Structures and Integrability of Frobenius Algebra-Valued (n, m)th KdV Hierarchy
Authors
Hai Zhang
School of Mathematical and Computational Science, Anqing Normal University Anqing, 246133, China,haizhang@mail.ustc.edu.cn
Received 14 December 2016, Accepted 20 March 2017, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2017.1341695How to use a DOI?
- Keywords
- ℱ-valued (n, m)th KdV hierarchy; Hamiltonian structure; hereditary recursion operator; flow equation
- Abstract
We introduce Frobenius algebra ℱ-valued (n, m)th KdV hierarchy and construct its bi-Hamiltonian structures by employing ℱ-valued pseudo-differential operators. As an illustrative example, the (1, 1)th 𝒵2-valued case is analyzed in detail. Its Hamiltonian structures and recursion operator are derived. Infinitely many symmetries, conservation laws and explicit flow equations are also obtained.
- Copyright
- © 2017 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 - Hai Zhang PY - 2021 DA - 2021/01/06 TI - Hamiltonian Structures and Integrability of Frobenius Algebra-Valued (n, m)th KdV Hierarchy JO - Journal of Nonlinear Mathematical Physics SP - 315 EP - 327 VL - 24 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2017.1341695 DO - 10.1080/14029251.2017.1341695 ID - Zhang2021 ER -