Geodesic
On the multicomponent nonlinear Schr\"odinger equation in the case of non-vanishing boundary conditions
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 4, Tome 131 (1983), pp. 34-46

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The inverse scattering transform is applied to the analysis of the multicomponent non-linear Schrödinger equation in the class of $s\times s$ matrix-valued functions $q(x)$, $\lim_{x\to\pm\infty}q(x)=q_\pm$, $q_+q_+^+=q_-q_-^+$. A number of peculiarities, due to the non-vanishing boundary conditions are exhibited, including: i) the existence of several chemical potentials; ii) the modifications in the integrals of motion and the Poisson brackets between the scattering data. 
@article{ZNSL_1983_131_a3,
     author = {V. S. Gerdjikov and P. P. Kulish},
     title = {On the multicomponent nonlinear {Schr\"odinger} equation in the case of non-vanishing boundary conditions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {34--46},
     publisher = {mathdoc},
     volume = {131},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_131_a3/}
}
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V. S. Gerdjikov; P. P. Kulish. On the multicomponent nonlinear Schr\"odinger equation in the case of non-vanishing boundary conditions. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 4, Tome 131 (1983), pp. 34-46. http://geodesic.mathdoc.fr/item/ZNSL_1983_131_a3/