Geodesic
Boundary-value problem for nonlinear Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 3, pp. 334-346

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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. 
@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},
     publisher = {mathdoc},
     volume = {79},
     number = {3},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_79_3_a1/}
}
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P. N. Bibikov; V. O. Tarasov. Boundary-value problem for nonlinear Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 79 (1989) no. 3, pp. 334-346. http://geodesic.mathdoc.fr/item/TMF_1989_79_3_a1/