Geodesic
Boundary-value problem for nonlinear Schrödinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 3, pp. 334-346 
P. N. Bibikov; V. O. Tarasov. Boundary-value problem for nonlinear Schrödinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 3, pp. 334-346. http://geodesic.mathdoc.fr/item/TMF_1989_79_3_a1/
@article{TMF_1989_79_3_a1,
     author = {P. N. Bibikov and V. O. Tarasov},
     title = {Boundary-value problem for nonlinear {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {334--346},
     year = {1989},
     volume = {79},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_79_3_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The boundary value problem on the half-line for the nonlinear Schrödinger equation (NLS) and its generalization is studied by means of the inverse scattering transform method. Connection between conservation laws and boundary conditions for the integrable boundary values for higher NLS equations is established. It is shown that the generalized boundary value problem needs the consideration of both regular and singular solution of NLS equations in the repulsive case.

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