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A proper formulation of restricted flows of soliton hierarchies associated with the first-order matrix spectral problem is given. They define completely integrable finite-dimensional systems invariant with respect to the action of all flows of the hierarchy. The first few restricted flows of the AKNS N=1,2 hierarchies are discussed in greater detail. They appear to be multiwave interaction systems.
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Ragnisco et al. (1992) studied this question.
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