Geodesic
Darboux transformation for the nonstationary Schr\"odinger equation
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 18, Tome 317 (2004), pp. 94-104

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A Lax representation for the nonstationary Schrödinger equation with rather arbitrary potential is proposed. Some examples of the construction of exact solutions are given by means of Darboux transformation method. 
@article{ZNSL_2004_317_a5,
     author = {E. Sh. Gutshabash},
     title = {Darboux transformation for the nonstationary {Schr\"odinger} equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {94--104},
     publisher = {mathdoc},
     volume = {317},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_317_a5/}
}
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E. Sh. Gutshabash. Darboux transformation for the nonstationary Schr\"odinger equation. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 18, Tome 317 (2004), pp. 94-104. http://geodesic.mathdoc.fr/item/ZNSL_2004_317_a5/