Geodesic
Solitons of the nonlinear Schrödinger equation generated by the continuum
Teoretičeskaâ i matematičeskaâ fizika, Tome 68 (1986) no. 2, pp. 172-186 
V. P. Kotlyarov; E. Ya. Khruslov. Solitons of the nonlinear Schrödinger 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/
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     title = {Solitons of the nonlinear {Schr\"odinger} equation generated by the continuum},
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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.

[1] Gurevich A. V., Pitaevskii L. P., Pisma v ZhETF, 17 (1973), 268–271

[2] Gurevich A. V., Pitaevskii L. P., ZhETF, 65 (1973), 590–604

[3] Khruslov E. Ya., Pisma v ZhETF, 21 (1975), 469–472; Матем. сб., 99 (1976), 261–281 | MR | Zbl

[4] Ermakova V. D., DAN USSR, ser. A, 7 (1982), 3–6 | MR | Zbl

[5] Its A. R., Kotlyarov V. P., DAN USSR, ser. A, 11 (1976), 965–968 | MR

[6] Zakharov V. E., Shabat A. B., ZhETF, 61 (1971), 118–134 | MR

[7] Its A. R., Vestn. LGU, matem., mekh., astr., 1976, no. 7, 39–46 | MR | Zbl

[8] Matveev V. B., Abelian functions and solitons, Preprint University of Wroclaw No 373, Wroclaw, 1976

[9] Fedoryuk M. V., Metod perevala, Nauka, M., 1977 | MR