Geodesic
Reflectionless potentials and soliton series of the KDV equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 2, pp. 286-301

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Potentials of the Schrödinger equation, slowly decreasing at infinity, generate an infinite discrete spectrum converging to zero. The inverse scattering problem in the class of such potentials is solved in a constructive way similarly to the classical soliton theory. An infinite-dimensional system arising from Backlund transformations over soliton solutions plays the role of a determinant representation of the potential. The asymptotics at infinity is derived by use of the Poisson summation formula. An application to the long-time asymptotics of the solution of the Korteweg-de Vries equation is considered. 
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     author = {V. Yu. Novokshenov},
     title = {Reflectionless potentials and soliton series of the {KDV} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {286--301},
     publisher = {mathdoc},
     volume = {93},
     number = {2},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_93_2_a7/}
}
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V. Yu. Novokshenov. Reflectionless potentials and soliton series of the KDV equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 2, pp. 286-301. http://geodesic.mathdoc.fr/item/TMF_1992_93_2_a7/