Geodesic
On the Transformations of Symplectic Expansions and the Respective Bäcklund Transformation for the KDV Equation
Serdica Mathematical Journal, Tome 29 (2003) no. 1, pp. 75-94.

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By using the Deift–Trubowitz transformations for adding or removing bound states to the spectrum of the Schrödinger operator on the line we construct a simple algorithm allowing one to reduce the problem of deriving symplectic expansions to its simplest case when the spectrum is purely continuous, and vice versa. We also obtain the transformation formulas for the correponding recursion operator. As an illustration of this approach, the Bäcklund transformations for the KdV equation are constructed.
Keywords: Symplectic Expantion, KdV Equation, Bäcklund Transformation 
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Khristov, E. On the Transformations of Symplectic Expansions and the Respective Bäcklund Transformation for the KDV Equation. Serdica Mathematical Journal, Tome 29 (2003) no. 1, pp. 75-94. http://geodesic.mathdoc.fr/item/SMJ2_2003_29_1_a6/