On improving the effectiveness of periodic solutions of the NLS and DNLS equations

A method for improving the effectiveness of one-phase periodic solutions of integrable equations is suggested, which is based on the explicit determination of the locus of the auxiliary spectrum point. The method is applied to the nonlinear Schrodinger equation a n d the derivative nonlinear Schrodinger equation. I t is shown that the relations between polynomial P ( A), defining the solution in the incerse transform method, and its algebraic resolvents play an important role in the theory. 1.