Integration of the loaded negative order nonlinear Schrodinger equation in the class of periodic functions

In this paper, we consider the loaded negative order nonlinear Schrodinger equation (NSE) in the class of periodic functions. It is shown that the loaded negative order nonlinear Schrodinger equation 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 loaded negative order nonlinear Schrodinger equation is determined. The results obtained make it possible to apply the inverse problem method to solve the loaded negative order nonlinear Schrodinger equation in the class of periodic ones. Important corollaries are obtained about the analyticity and period of the solution concerning the spatial variable.