Dubrovin’s method and Ablowitz-Kaup-Newell-Segur hierarchy

Abstract

Abstract Previously, the Dubrovin method was used to construct spectral curves of multiphase solutions of such integrable models of nonlinear optics as vector and derived nonlinear Schrödinger equations. The method of constructing spectral curves of multiphase solutions of the scalar nonlinear Schrödinger equation was based on replacing matrix differential operator from the Lax pair by the scalar one. The present paper shows that Dubrovin’s method gives the same results. At the same time, it has the advantage that it consists in a simpler construction of multiphase solutions expressed in terms of elementary functions.