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Restricted flows of soliton hierarchies associated with the energy-dependent Schrodinger spectral problem are determined explicitly. A remarkable connection with separable potentials is used for proving complete integrability of the restricted flows. A previously unknown Lagrangian and Hamiltonian formulation of the Neumann system is found. Whole families of generalizations of the Neumann and Garnier systems are given.
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Antonowicz et al. (1991) studied this question.
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