Geodesic
Application of inverse scattering method to singular solutions of nonlinear equations.~I
Teoretičeskaâ i matematičeskaâ fizika, Tome 53 (1982) no. 2, pp. 163-180

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The Jost solutions and the transition matrix for the Zakharov–Shabat system are constructed in the case of potentials that have a finite number of $x^{-1}$ singularities. The analytic properties of the transition matrix are investigated and scattering data are introduced. 
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     author = {V. A. Arkad'ev and A. K. Pogrebkov and M. K. Polivanov},
     title = {Application of inverse scattering method to singular solutions of nonlinear {equations.~I}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {53},
     number = {2},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1982_53_2_a0/}
}
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V. A. Arkad'ev; A. K. Pogrebkov; M. K. Polivanov. Application of inverse scattering method to singular solutions of nonlinear equations.~I. Teoretičeskaâ i matematičeskaâ fizika, Tome 53 (1982) no. 2, pp. 163-180. http://geodesic.mathdoc.fr/item/TMF_1982_53_2_a0/