Integration of the Negative Order Nonlinear Schrödinger Equation in the Class of Periodic Functions

In this paper, we study the negative order nonlinear Schrödinger equation. It is shown that the nonlinear Schrödinger equation of negative order can be integrated by the inverse spectral problem method. The evolution of the spectral data of the Dirac operator with a periodic potential associated with the solution of the negative order nonlinear Schrödinger equation is determined. Obtained results make it possible to apply the inverse problem method to solve the negative order nonlinear Schrödinger equation in the class of periodic functions. Important consequences about the construction algorithm of the solution are provided.