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Dubrovin type equations for the N -gap solution of a completely
integrable system associated with a polynomial pencil is constructed and
then integrated to a system of functional equations. The approach used to
derive those results is a generalization of the familiar process of finding the
1-soliton (1-gap) solution by integrating the ODE obtained from the soliton
equation via the substitution u = u(x + λt).
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