Geodesic
Continuity of the Scattering Transformation for the Korteweg de Vries Equation
Canadian journal of mathematics, Tome 38 (1986) no. 2, pp. 360-375

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It is at present well known that, if q(x, t) is a solution of the Korteweg de Vries (K d V) equation (1) such that q(x, 0) = q 0(x), where q 0(x) behaves reasonably at infinity, and if are the scattering data (see [4]) corresponding to q(x, t), then 
Gautrin, Henri-François; Klemola, Tapio. Continuity of the Scattering Transformation for the Korteweg de Vries Equation. Canadian journal of mathematics, Tome 38 (1986) no. 2, pp. 360-375. doi: 10.4153/CJM-1986-017-4
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[1] 1. Ablowitz, M. J. and Segur, H., Solitons and the inverse scattering transform, SIAM (1981). Google Scholar | DOI

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