Geodesic
Solitons of the nonlinear Schr\"odinger equation generated by the continuum
Teoretičeskaâ i matematičeskaâ fizika, Tome 68 (1986) no. 2, pp. 172-186

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A study is made of the large-time asymptotic behavior of the solutions of the nonlinear Schrödinger equation with attraction that tend to zero as $x\to+\infty$ and to a finite-gap solution of the equation as $x\to-\infty$. It is shown that in the region of the leading edge such solutions decay in the limit $t\to\infty$ into an infinite series of solitons with variable phases, the solitons being generated by the continuous spectrum of the operator $L$ of the corresponding Lax pair. 
@article{TMF_1986_68_2_a1,
     author = {V. P. Kotlyarov and E. Ya. Khruslov},
     title = {Solitons of the nonlinear {Schr\"odinger} equation generated by the continuum},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {172--186},
     publisher = {mathdoc},
     volume = {68},
     number = {2},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1986_68_2_a1/}
}
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V. P. Kotlyarov; E. Ya. Khruslov. Solitons of the nonlinear Schr\"odinger equation generated by the continuum. Teoretičeskaâ i matematičeskaâ fizika, Tome 68 (1986) no. 2, pp. 172-186. http://geodesic.mathdoc.fr/item/TMF_1986_68_2_a1/