Geodesic
Solution of the Benney equations by the inverse scattering method
Teoretičeskaâ i matematičeskaâ fizika, Tome 73 (1987) no. 2, pp. 255-263

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Quasiclassical limit of the method of inverse scattering problem is developed for the Benney equations (which describe non-potential waves in a shallow liquid), the liquid being divided into layers, each with its own velocity. The solution of the Cauchy problem for these equations is given by algebraic formulas. 
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     author = {V. V. Geogdzhaev},
     title = {Solution of the {Benney} equations by the inverse scattering method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {255--263},
     publisher = {mathdoc},
     volume = {73},
     number = {2},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1987_73_2_a8/}
}
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V. V. Geogdzhaev. Solution of the Benney equations by the inverse scattering method. Teoretičeskaâ i matematičeskaâ fizika, Tome 73 (1987) no. 2, pp. 255-263. http://geodesic.mathdoc.fr/item/TMF_1987_73_2_a8/