Generalized negative flows in hierarchies of integrable evolution equations |
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| Authors: | Stephen C Anco Shahid Mohammad Thomas Wolf Chunrong Zhu |
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| Institution: | 1. Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S3A1, Canada;2. Department of Mathematics, Central Michigan University, Mount Pleasant, MI 48859, USA;3. College of Mathematics and Computer Science, Anhui Normal University, Wuhu, Anhui 241000, China |
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| 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. |
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| Keywords: | integrable equation negative flow bi-Hamiltonian |
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