The Kulish-Sklyanin type hierarchy and spectral curves

Abstract

Abstract A poorly studied version of the three-component vector nonlinear Schrodinger equation, called the Kulish-Sklyanin model, is considered. Using the Dubrovin method, we obtain recurrent relations that allow us to obtain all equations from the corresponding hierarchy. The first two equations of the Kulish-Sklyanin hierarchy are found. It follows from these equations that the Kulish-Sklyanin model is associated with a rather non-trivial nonlinear interaction of the solution components. In particular, it is shown that the behavior of the third component of the solution of equations from the Kulish-Sklyanin hierarchy is completely determined by the parameters of the other two components. The equation of the spectral curve of the solution in the form of a plane wave is obtained.