Journal of Nonlinear Mathematical Physics

Volume 23, Issue 4, September 2016, Pages 573 - 606

Generalized negative flows in hierarchies of integrable evolution equations

Authors
Stephen C. Anco1, Shahid Mohammad1, 2, Thomas Wolf1, Chunrong Zhu1, 3
1Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S3A1, Canada, sanco@brocku.ca, twolf@brocku.ca
2Department of Mathematics, Central Michigan University, Mount Pleasant, MI 48859, USA, moham3s@cmich.edu
3College of Mathematics and Computer Science, Anhui Normal University, Wuhu, Anhui 241000, China, zcr2009@mail.ahnu.edu.cn
Received 28 May 2016, Accepted 9 September 2016, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2016.1248157How to use a DOI?
Keywords
integrable equation, negative flow, bi-Hamiltonian
Abstract

A one-parameter generalization of the hierarchy of negative flows is introduced for integrable hierarchies of evolution equations, which yields a wider (new) class of non-evolutionary integrable nonlinear wave equations. As main results, several integrability properties of these generalized negative flow equation are established, including their symmetry structure, conservation laws, and bi-Hamiltonian formulation. (The results also apply to the hierarchy of ordinary negative flows). The first generalized negative flow equation is worked out explicitly for each of the following integrable equations: Burgers, Korteweg-de Vries, modified Korteweg-de Vries, Sawada-Kotera, Kaup-Kupershmidt, Kupershmidt.

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 - 4
Pages
573 - 606
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2016.1248157How 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  - Stephen C. Anco
AU  - Shahid Mohammad
AU  - Thomas Wolf
AU  - Chunrong Zhu
PY  - 2021
DA  - 2021/01
TI  - Generalized negative flows in hierarchies of integrable evolution equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 573
EP  - 606
VL  - 23
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2016.1248157
DO  - https://doi.org/10.1080/14029251.2016.1248157
ID  - Anco2021
ER  -