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A Liouville integrable Hamiltonian system associated with a generalized Kaup-Newell spectral problem. (English) Zbl 0977.37039

Summary: Starting from a generalized Kaup-Newell spectral problem involving an arbitrary function, we derive a hierarchy of nonlinear evolution equations, which is explicitly related to many important equations such as Kaup-Newell equation, Chen-Lee-Liu equation, Gerdjikov-Ivanov equation, Burgers equation, modified Korteweg-de Vries equation and Sharma-Tasso-Olever equation. It is also shown that the hierarchy is integrable in Liouville’s sense and possesses multi-Hamiltonian structure.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q53 KdV equations (Korteweg-de Vries equations)
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