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Application of inverse scattering method to singular solutions of nonlinear equations. III
Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 1, pp. 38-49 Cet article a éte moissonné depuis la source Math-Net.Ru

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An existence and uniqueness theorem is proved for the solution of the Cauchy problem for the nonlinear Schrödinger equation with repulsion in the class of functions with singularities of the type $x^{-1}$. The behavior of the singularity lines of the solution in the $(x,t)$ plane is described. 
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     author = {V. A. Arkad'ev},
     title = {Application of inverse scattering method to singular solutions of nonlinear equations. {III}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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}
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V. A. Arkad'ev. Application of inverse scattering method to singular solutions of nonlinear equations. III. Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 1, pp. 38-49. http://geodesic.mathdoc.fr/item/TMF_1984_58_1_a2/

[1] Arkadev V. A., Pogrebkov A. K., Polivanov M. K., TMF, 53:2 (1982), 163–180 | MR

[2] Arkadev V. A., Pogrebkov A. K., Polivanov M. K., TMF, 54:1 (1983), 23–37 | MR | Zbl

[3] S. P. Novikov (red.), Teoriya solitonov: Metod obratnoi zadachi, Nauka, M., 1980, 320 pp. | MR