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TMF, 2015, Volume 185, Number 2, Pages 272–288 (Mi tmf8982)  

This article is cited in 2 scientific papers (total in 2 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

Abstract: We describe the properties of the Cauchy–Jost (also known as Cauchy–Baker–Akhiezer) function of the Kadomtsev–Petviashvili-II equation. Using the $\bar\partial$-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.


DOI: https://doi.org/10.4213/tmf8982

Full text: PDF file (447 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 185:2, 1599–1613

Bibliographic databases:

Document Type: Article
Received: 30.04.2015

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Andrei K. Pogrebkov, “Symmetries of the Hirota Difference Equation”, SIGMA, 13 (2017), 053, 14 pp.  mathnet  crossref  mathscinet
    2. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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