Geodesic
Kdv flow on generalized reflectionless potentials
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (2008), pp. 490-528

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The purpose of this article is to construct KdV flow on a space of generalized reflectionless potentials by applying Sato's Grassmannian approach. The point is that the base space contains not only rapidly decreasing potentials but also oscillating ones such as periodic ones, which makes it possible for us to discuss the shift invariant probability measures on it. 
@article{JMAG_2008_4_a2,
     author = {S. Kotani},
     title = {Kdv flow on generalized reflectionless potentials},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {490--528},
     publisher = {mathdoc},
     volume = {4},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2008_4_a2/}
}
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S. Kotani. Kdv flow on generalized reflectionless potentials. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (2008), pp. 490-528. http://geodesic.mathdoc.fr/item/JMAG_2008_4_a2/