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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, Volume 31, Issue 2, Pages 285–295
DOI: https://doi.org/10.35634/vm210209 (Mi vuu770) 		 
This article is cited in 5 scientific papers (total in 5 papers)

MATHEMATICS

Integration of the Harry Dym equation with an integral type source

G. U. Urazboevab, A. K. Babadjanovab, D. R. Saparbaevaa

a Urgench State University, ul. Khamida Alimdjana, 14, Urgench, 220100, Uzbekistan
b V. I. Romanovskiy Institute of Mathematics, Khorezm branch of Uzbekistan Academy of Sciences, ul. Khamida Alimdjana, 14, Urgench, 220100, Uzbekistan
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DOI: https://doi.org/10.35634/vm210209
Abstract: In the work, we deduce the evolution of scattering data for a spectral problem associated with the nonlinear evolutionary equation of Harry Dym with a self-consistent source of integral type. The obtained equalities completely determine the scattering data for any $t$, which makes it possible to apply the method of the inverse scattering problem to solve the Cauchy problem for the Harry Dym equation with an integral type source.
Keywords: nonlinear evolution equation, Harry Dym equation, integral source, inverse scattering method, Gelfand–Levitan–Marchenko equation.
Received: 24.12.2020
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: 34L25, 35Q41, 37K10, 35R30, 34M46
Language: English
Citation: G. U. Urazboev, A. K. Babadjanova, D. R. Saparbaeva, “Integration of the Harry Dym equation with an integral type source”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:2 (2021), 285–295
Citation in format AMSBIB
\Bibitem{UraBabSap21}
\by G.~U.~Urazboev, A.~K.~Babadjanova, D.~R.~Saparbaeva
\paper Integration of the Harry Dym equation with an integral type source
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2021
\vol 31
\issue 2
\pages 285--295
\mathnet{http://mi.mathnet.ru/vuu770}
\crossref{https://doi.org/10.35634/vm210209}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000668895900009}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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