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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 206, Number 3, Pages 339–360
DOI: https://doi.org/10.4213/tmf9988 (Mi tmf9988) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (499 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf9988
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 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
English version:
Theoretical and Mathematical Physics, 2021, Volume 206, Issue 3, Pages 296–314
DOI: https://doi.org/10.1134/S004057792103003X
Bibliographic databases:
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf9988
  • https://doi.org/10.4213/tmf9988
  • https://www.mathnet.ru/eng/tmf/v206/i3/p339
    • This publication is cited in the following 2 articles:
    1. G. F. Helminck, V. A. Poberezhny, S. V. Polenkova, “Darboux transformations for the discrete versions of the KP and strict KP hierarchies”, Theoret. and Math. Phys., 221:3 (2024), 2031–2048  mathnet  crossref  crossref  adsnasa
    2. Yuru Hu, Feng Zhang, Xiangpeng Xin, Hanze Liu, “Darboux transformation and exact solutions of the variable-coefficient nonlocal Gerdjikov–Ivanov equation”, Theoret. and Math. Phys., 211:1 (2022), 460–472  mathnet  crossref  crossref  mathscinet  adsnasa
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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