Generalized negative flows in hierarchies of integrable evolution equations

Anco, Stephen C.; Mohammad, Shahid; Wolf, Thomas; Zhu, Chunrong

doi:10.1080/14029251.2016.1248157

Generalized negative flows in hierarchies of integrable evolution equations

Oct 14, 2016

34 pages

Published in:

J.Nonlin.Math.Phys. 23 (2016) 4, 573-606

Published: Oct 14, 2016

DOI:

10.1080/14029251.2016.1248157

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Abstract: (Taylor and Francis)

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.

integrable equation
negative flow
bi-Hamiltonian

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