Generalized negative flows in hierarchies of integrable evolution equations
- 10.1080/14029251.2016.1248157How to use a DOI?
- integrable equation; negative flow; bi-Hamiltonian
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.
- © 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 - 2021/01/06 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 - 10.1080/14029251.2016.1248157 ID - Anco2021 ER -