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arXiv · 1604.07779

Generalized negative flows in hierarchies of integrable evolution equations

Stephen C. Anco·Shahid Mohammad·Thomas Wolf·Chunrong Zhu
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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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Stephen C. Anco, Shahid Mohammad, Thomas Wolf, Chunrong Zhu. 2016-04-26. Generalized negative flows in hierarchies of integrable evolution equations. https://arxiv.org/abs/1604.07779

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