Geodesic
Darboux transformations for the~strict KP hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 206 (2021) no. 3, pp. 339-360

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We introduce the notion of Darboux transformations for the strict KP hierarchy. We previously showed that solutions of this integrable hierarchy can be constructed from a flag variety $\mathcal{F}(1)$. Here, we describe which two points in this flag variety are connected by such a transformation. Moreover, we present a closed form of the operators that realize this transformation and describe their geometric characteristics. We show which of these Darboux transformations map solutions of the strict $n$-KdV hierarchy to other solutions of this reduction of the strict KP hierarchy.
Keywords: pseudodifferential operator, (strict) KP hierarchy, (dual) linearization, (dual) oscillating function, (dual) wave function
Mots-clés : Darboux transformation. 
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     author = {G. F. Helminck and E. A. Panasenko},
     title = {Darboux transformations for the~strict {KP} hierarchy},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {339--360},
     publisher = {mathdoc},
     volume = {206},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_206_3_a2/}
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G. F. Helminck; E. A. Panasenko. Darboux transformations for the~strict KP hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 206 (2021) no. 3, pp. 339-360. http://geodesic.mathdoc.fr/item/TMF_2021_206_3_a2/