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Algebra i Analiz, 2022, Volume 34, Issue 5, Pages 139–172 (Mi aa1833)  

This article is cited in 8 scientific papers (total in 8 papers)

Research Papers

The Cauchy problem for a nonlinear Hirota equation in the class of periodic infinite-zone functions

G. A. Mannonov, A. B. Khasanov

Samarkand State University
References:
Abstract: The method of inverse spectral problem is used to integrate the nonlinear Hirota equation in the class of periodic infinite-zone functions. The evolution of spectral data is introduced for the periodic Dirac operator whose coefficient is the solution of the nonlinear Hirota equation. The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of five times continuously differentiable periodic infinite-zone functions is shown. In addition, it is proved that if the initial function is real-analytic and $\pi$-periodic, then the solution of the Cauchy problem for the Hirota equation is also a real-analytic function of the variable $x$; next, if the number $\pi/2$ is a period (antiperiod) of the initial function, then the number $\pi/2$ is a period (antiperiod) in the variable $x$ for the solution of the Cauchy problem for the Hirota equation.
Keywords: Hirota equation, Dirac operator, Spectral data, Dubrovin system, trace formulas.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation НШ-0000.0000.0
Received: 15.02.2022
English version:
St. Petersburg Mathematical Journal, 2023, Volume 34, Issue 5, Pages 821–845
DOI: https://doi.org/10.1090/spmj/1780
Document Type: Article
Language: Russian
Citation: G. A. Mannonov, A. B. Khasanov, “The Cauchy problem for a nonlinear Hirota equation in the class of periodic infinite-zone functions”, Algebra i Analiz, 34:5 (2022), 139–172; St. Petersburg Math. J., 34:5 (2023), 821–845
Citation in format AMSBIB
\Bibitem{ManKha22}
\by G.~A.~Mannonov, A.~B.~Khasanov
\paper The Cauchy problem for a nonlinear Hirota equation in the class of periodic infinite-zone functions
\jour Algebra i Analiz
\yr 2022
\vol 34
\issue 5
\pages 139--172
\mathnet{http://mi.mathnet.ru/aa1833}
\transl
\jour St. Petersburg Math. J.
\yr 2023
\vol 34
\issue 5
\pages 821--845
\crossref{https://doi.org/10.1090/spmj/1780}
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  • https://www.mathnet.ru/eng/aa/v34/i5/p139
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и анализ St. Petersburg Mathematical Journal
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    Full-text PDF :11
    References:32
    First page:15
     
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