Geodesic
Lattice dark solitons in the linear potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 413-418

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We deal with the nonlinear lattice$$i\dot {\psi }_n+(1-|\psi _n|^2)( \psi _{n+1}+ \psi _{n-1}-2\psi _n)+2(\rho ^2-|\psi _n|^2)\psi _n+\gamma n\psi _n=0$$ subject to the finite density boundary conditions. It is shown that it is integrable by means of the inverse scattering technique. Soliton solutions undergo periodic motion with the frequency $\gamma$. Small amplitude limit of the model is discussed. 
@article{TMF_1994_99_3_a8,
     author = {V. V. Konotop},
     title = {Lattice dark solitons in the linear potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {413--418},
     publisher = {mathdoc},
     volume = {99},
     number = {3},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a8/}
}
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V. V. Konotop. Lattice dark solitons in the linear potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 3, pp. 413-418. http://geodesic.mathdoc.fr/item/TMF_1994_99_3_a8/