Generalized negative flows in hierarchies of integrable evolution equations
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.
Cite
@article{arxiv.1604.07779,
title = {Generalized negative flows in hierarchies of integrable evolution equations},
author = {Stephen C. Anco and Shahid Mohammad and Thomas Wolf and Chunrong Zhu},
journal= {arXiv preprint arXiv:1604.07779},
year = {2017}
}
Comments
31 pages. More references and added comparison with negative flow equations in literature. Published version