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INTEGRATION OF A NONLINEAR SCHRÖDINGER EQUATION OF NEGATIVE ORDER WITH A SELF-CONSISTENT SUM SOURCE
In this paper, we consider a negative-order nonlinear Schrödinger equation (NSE) with a self-consistent sum source. We show that the NSE with a self-consistent sum source can be integrated using the inverse spectral problem method. We also determine the evolution of the spectral data for the Dirac operator with a periodic potential associated with the solution of the NSE with a self-consistent sum source. The results obtained allow us to apply the inverse problem method to solving the NSE with a self-consistent sum source. Important implications regarding the analyticity and period of the solution with respect to the spatial variable are obtained.