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Restricted Flows and the Soliton Equation with Self-Consistent Sources
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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The KdV equation is used as an example to illustrate the relation between the restricted flows and the soliton equation with self-consistent sources. Inspired by the results on the Bäcklund transformation for the restricted flows (by V. B. Kuznetsov et al.), we constructed two types of Darboux transformations for the KdV equation with self-consistent sources (KdVES). These Darboux transformations are used to get some explicit solutions of the KdVES, which include soliton, rational, positon, and negaton solutions.
Keywords: the KdV equation with self-consistent sources; restricted flows; Lax pair; Darboux transformation; soliton solution. 
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Runliang Lin; Haishen Yao; Yunbo Zeng. Restricted Flows and the Soliton Equation with Self-Consistent Sources. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a95/

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