Geodesic
B\"acklund and Darboux Transformations for the Nonstationary Schr\"odinger Equation
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics. Problems of quantum field theory, Tome 226 (1999), pp. 49-71

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Potentials of the nonstationary Schrödinger operator constructed by means of $n$ recursive Bäcklund transformations are studied in detail. The corresponding Darboux transformations of the Jost solutions are introduced. We show that these solutions obey modified integral equations and present their analyticity properties. Generated transformations of the spectral data are derived. 
@article{TM_1999_226_a4,
     author = {M. Boiti and F. Pempinelli and A. K. Pogrebkov and B. Prinari},
     title = {B\"acklund and {Darboux} {Transformations} for the {Nonstationary} {Schr\"odinger} {Equation}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {49--71},
     publisher = {mathdoc},
     volume = {226},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_1999_226_a4/}
}
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M. Boiti; F. Pempinelli; A. K. Pogrebkov; B. Prinari. B\"acklund and Darboux Transformations for the Nonstationary Schr\"odinger Equation. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics. Problems of quantum field theory, Tome 226 (1999), pp. 49-71. http://geodesic.mathdoc.fr/item/TM_1999_226_a4/