Geodesic
Factorization and Poisson correspondences
Teoretičeskaâ i matematičeskaâ fizika, Tome 105 (1995) no. 2, pp. 225-245

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The Darboux transformation as an example of an integrable infinite-dimensional Poisson correspondence is discussed in the context of the general factorization problem. Generalizations related to energy dependent Schrödinger operators and to Kac–Moody algebras are considered. We also present the finite dimensional reductions of the Darboux transformation to stationary flows. 
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     author = {A. P. Fordy and A. B. Shabat and A. P. Veselov},
     title = {Factorization and {Poisson} correspondences},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {105},
     number = {2},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_105_2_a4/}
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A. P. Fordy; A. B. Shabat; A. P. Veselov. Factorization and Poisson correspondences. Teoretičeskaâ i matematičeskaâ fizika, Tome 105 (1995) no. 2, pp. 225-245. http://geodesic.mathdoc.fr/item/TMF_1995_105_2_a4/