Geodesic
Nonlinear scattering: the states which are close to a soliton
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 24, Tome 200 (1992), pp. 38-50

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It is assumed that nonlinear Schroedinger equation with general nonlinearity admits solutions of the soliton's type. The Cauchy problem with the initial datum which is close to a soliton is considered. It is also assumed that the linearization of the equation on the soliton possesses only real spectrum. The main result claims that the asymptotic behavior of the solution as $t\to+\infty$ is given by the sum of a soliton with deformed parameters and a dispersive tail, i.e. a solution of the linear Schroedinger equation. In the previous work the case of the minimal spectrum has been considered. 
@article{ZNSL_1992_200_a3,
     author = {V. S. Buslaev and G. S. Perelman},
     title = {Nonlinear scattering: the states which are close to a soliton},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {38--50},
     publisher = {mathdoc},
     volume = {200},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_200_a3/}
}
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V. S. Buslaev; G. S. Perelman. Nonlinear scattering: the states which are close to a soliton. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 24, Tome 200 (1992), pp. 38-50. http://geodesic.mathdoc.fr/item/ZNSL_1992_200_a3/