Geodesic
Formulation of the scattering theory for the NLS equation with boundary conditions of the type of finite density in the soliton-free sector
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 8, Tome 169 (1988), pp. 60-67

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In terms of the spectral data for the auxiliary linear operator, under the assumption that there is no discrete spectrum, an asymptotic canonical variables and classical $S$-matrix for the ELS model with non-zero boundary conditions are calculatid. 
@article{ZNSL_1988_169_a6,
     author = {A. R. Its and A. F. Ustinov},
     title = {Formulation of the scattering theory for the {NLS} equation with boundary conditions of the type of finite density in the soliton-free sector},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {60--67},
     publisher = {mathdoc},
     volume = {169},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_169_a6/}
}
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A. R. Its; A. F. Ustinov. Formulation of the scattering theory for the NLS equation with boundary conditions of the type of finite density in the soliton-free sector. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 8, Tome 169 (1988), pp. 60-67. http://geodesic.mathdoc.fr/item/ZNSL_1988_169_a6/