Abstract
A spectral problem and the associated hierarchy of Schrodinger type equations are proposed. It is shown that the hierarchy is integrable in Liouville's sense and possesses multi-Hamiltonian structure. It is found that several kinds of important equation such as the Kaup-Newell (KN) equation, the Chen-Lee-Liu (CLL) equation, the Gerdjikov-Ivanov (GI) equation, the modified Korteweg-de Vries equation and the Sharma-Tasso-Olever equation are members in the hierarchy as its special reductions. Moreover, KN, CLL and GI equations are described by using a unified generalized derivative Schrodinger equation involving a parameter, and their Hamiltonian structure and Lax pairs are also given by unified and explicit formulae.
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