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The authors give a solution to the problem of finding a spectral parameter dependent Lax representation for restricted flows of matrix Lax equations by constructing first a Lax representation for soliton hierarchies with sources. Its stationary flows (the restricted flows) naturally possess a Lax representation which can be made local. The general results are exemplified by restricted flows of matrix Schrodinger and AKNS hierarchies.
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Antonowicz et al. (1993) studied this question.
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