Geodesic
The influence of perturbation upons solitons of some nonlinear equations
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 10, Tome 89 (1979), pp. 91-96

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The problems of the influence of the perturbations on the soliton solutions of some nonlinear equations are considered. The author shows that the relations for the shift (of the coordinate) and velocity of solitons can be got in the elementary way, without using the inverse scattering theory. 
@article{ZNSL_1979_89_a6,
     author = {S. A. Vakulenko},
     title = {The influence of perturbation upons solitons of some nonlinear equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {91--96},
     publisher = {mathdoc},
     volume = {89},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_89_a6/}
}
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S. A. Vakulenko. The influence of perturbation upons solitons of some nonlinear equations. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 10, Tome 89 (1979), pp. 91-96. http://geodesic.mathdoc.fr/item/ZNSL_1979_89_a6/