Geodesic
Reflectionless potentials and soliton series of the KDV equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 2, pp. 286-301 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

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