Formulation of scattering theory for the nonlinear Schrödinger equation with boundary conditions of the finite density type in a soliton-free sector

Asymptotic canonical variables and the classical S matrix for the nonlinear Schrödinger model with nonzero boundary conditions are calculated in terms of spectral data of an auxiliary linear operator, subject to the condition that a discrete spectrum does not exist.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 60–67, 1988.