Geodesic
Exact integration of nonlinear Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 74 (1988) no. 1, pp. 29-45

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The degeneracy of finite-gap expressions is used to obtain a manyparameter family of smooth periodic and almost periodic solutions of the nonlinear Schrödinger equation in terms of elementary functions. A scheme for obtaining these solutions by the Darboux transformation method is considered. Propagation of a soliton on an arbitrary background is studied. 
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     author = {A. R. Its and A. V. Rybin and M. A. Sall'},
     title = {Exact integration of nonlinear {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {74},
     number = {1},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_74_1_a2/}
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A. R. Its; A. V. Rybin; M. A. Sall'. Exact integration of nonlinear Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 74 (1988) no. 1, pp. 29-45. http://geodesic.mathdoc.fr/item/TMF_1988_74_1_a2/