Generalized negative flows in hierarchies of integrable evolution equations. Issue 4 (1st October 2016)

• Record Type: Journal Article
• Authors: Anco, Stephen C.; Mohammad, Shahid; Wolf, Thomas; Zhu, Chunrong
• Is Part Of: Journal of nonlinear mathematical physics. Volume 23:Issue 4(2016)
• Page Start: 573
• Page End: 606
• Publication Date: 2016-10-01
• Subjects: integrable equation -- negative flow -- bi-Hamiltonian; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2016.1248157
• Languages: English
• ISSNs: 1402-9251

Abstract

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.