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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, Volume 32, Issue 2, Pages 153–170
DOI: https://doi.org/10.35634/vm220201 (Mi vuu804) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Integration of the Kaup-Boussinesq system with a self-consistent source via inverse scattering method

B. A. Babajanovab, A. Sh. Azamatova

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/vm220201
Abstract: In this study we consider the Kaup–Boussinesq system with a self-consistent source. We show that the Kaup–Boussinesq system with a self-consistent source can be integrated by the method of inverse scattering theory. For a solving the problem under consideration, we use the direct and inverse scattering problem of the Sturm–Liouville equation with an energy-dependent potential. The time evolution of the scattering data for the Sturm–Liouville equation with an energy-dependent potentials associated with the solution of the Kaup–Boussinesq system with a self-consistent source is determined. 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 Kaup–Boussinesq system with a self-consistent source.
Keywords: nonlinear soliton equation, Kaup–Boussinesq system, self-consistent source, inverse scattering method, quadratic pencil of Sturm–Liouville equations.
Received: 11.01.2022
Accepted: 06.05.2022
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: 34L25, 35Q41, 37K10, 35R30, 34M46
Language: English
Citation: B. A. Babajanov, A. Sh. Azamatov, “Integration of the Kaup-Boussinesq system with a self-consistent source via inverse scattering method”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 32:2 (2022), 153–170
Citation in format AMSBIB
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\by B.~A.~Babajanov, A.~Sh.~Azamatov
\paper Integration of the Kaup-Boussinesq system with a self-consistent source via inverse scattering method
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2022
\vol 32
\issue 2
\pages 153--170
\mathnet{http://mi.mathnet.ru/vuu804}
\crossref{https://doi.org/10.35634/vm220201}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4456913}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000851428400001}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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