INTEGRATION OF THE NONLINEAR SCHR\"{O}DINGER EQUATION WITH A SELF-CONSISTENT SOURCE AND NONZERO BOUNDARY CONDITIONS

This paper is devoted to the study of the defocusing nonlinear Schrödinger equation with a self-consistent source and nonzero boundary conditions by the method of the inverse scattering problem.In cases where the source consists of a combination of eigenfunctions of the corresponding spectral problem for the Zakharov-Shabat system, the complete integrability of the nonlinear Schrödinger equation is investigated.Namely, the evolutions of the scattering data of the self-adjoint Zakharov-Shabat system, whose potential is a solution of the defocusing nonlinear Schrödinger equation with a self-consistent source, are obtained.

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