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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 185, Number 2, Pages 272–288
DOI: https://doi.org/10.4213/tmf8982 (Mi tmf8982) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Cauchy–Jost function and hierarchy of integrable equations

M. Boitia, F. Pempinellia, A. K. Pogrebkovb

a EINSTEIN Consortium, Lecce, Italy
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Full-text PDF (447 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf8982
Abstract: We describe the properties of the Cauchy–Jost (also known as Cauchy–Baker–Akhiezer) function of the Kadomtsev–Petviashvili-II equation. Using the ˉ∂¯∂-method, we show that for this function, all equations of the Kadomtsev–Petviashvili-II hierarchy are given in a compact and explicit form, including equations for the Cauchy–Jost function itself, time evolutions of the Jost solutions, and evolutions of the potential of the heat equation.
Keywords: Cauchy–Jost function, KP-II equation, inverse problem.
Funding agency Grant number
Russian Science Foundation 14-50-00005
Sections 3, 4 and 5 of the article are performed by A. K. Pogrebkov, sections 1, 2 and 6 are performed by M. Boiti and F. Pempinelli. Investigation of A. K. Pogrebkov is carried out at the expense of the Russian Science Foundation (grant no. 14-50-00005) at Steklov Mathematical Institute of Russian Academy of Sciences.
Received: 30.04.2015
English version:
Theoretical and Mathematical Physics, 2015, Volume 185, Issue 2, Pages 1599–1613
DOI: https://doi.org/10.1007/s11232-015-0367-y
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. Boiti, F. Pempinelli, A. K. Pogrebkov, “Cauchy–Jost function and hierarchy of integrable equations”, TMF, 185:2 (2015), 272–288; Theoret. and Math. Phys., 185:2 (2015), 1599–1613
Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8982
  • https://www.mathnet.ru/eng/tmf/v185/i2/p272
    • This publication is cited in the following 3 articles:
    1. Wang X., Zhu J., Qiao Zh., “New Solutions to the Differential-Difference Kp Equation”, Appl. Math. Lett., 113 (2021), 106836  crossref  mathscinet  isi  scopus
    2. Andrei K. Pogrebkov, “Symmetries of the Hirota Difference Equation”, SIGMA, 13 (2017), 053, 14 pp.  mathnet  crossref  mathscinet
    3. M. Boiti, F. Pempinelli, A. K. Pogrebkov, “KPII: Cauchy-Jost ffunction, Darboux transformations and totally nonnegative matrices”, J. Phys. A-Math. Theor., 50:30 (2017), 304001  crossref  mathscinet  zmath  isi  scopus
    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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