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This article is cited in 1 scientific paper (total in 1 paper)
Darboux transformations for the strict KP hierarchy
G. F. Helmincka, E. A. Panasenkob a Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands
b Derzhavin State University, Tambov, Russia
Abstract:
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, Darboux transformation.
Received: 24.09.2020 Revised: 02.11.2020
Citation:
G. F. Helminck, E. A. Panasenko, “Darboux transformations for the strict KP hierarchy”, TMF, 206:3 (2021), 339–360; Theoret. and Math. Phys., 206:3 (2021), 296–314
Linking options:
https://www.mathnet.ru/eng/tmf9988https://doi.org/10.4213/tmf9988 https://www.mathnet.ru/eng/tmf/v206/i3/p339
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Abstract page: | 199 | Full-text PDF : | 44 | References: | 19 | First page: | 11 |
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