Geodesic
Backlund-Darboux Transformations in Sato's Grassmannian
Serdica Mathematical Journal, Tome 22 (1996) no. 4, pp. 571-586.

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We define Bäcklund–Darboux transformations in Sato’s Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the action of these transformations on related objects: wave functions, tau-functions and spectral algebras.
Keywords: Bäcklund–Darboux Transformation, Sato’s Grassmannian, Tau-Function, Spectral Algebra 
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     title = {Backlund-Darboux {Transformations} in {Sato's} {Grassmannian}},
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Bakalov, B.; Horozov, E.; Yakimov, M. Backlund-Darboux Transformations in Sato's Grassmannian. Serdica Mathematical Journal, Tome 22 (1996) no. 4, pp. 571-586. http://geodesic.mathdoc.fr/item/SMJ2_1996_22_4_a5/