Integrable systems of derivative nonlinear Schrodinger type and their multi-Hamiltonian structure

A spectral problem and the associated hierarchy of Schrodinger type equatio ns 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 Che n-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 equat ions are described by using a unified generalized derivative Schrodinger eq uation involving a parameter, and their Hamiltonian structure and Lax pairs are also given by unified and explicit formulae.