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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, Volume 33, Issue 1, Pages 156–170
DOI: https://doi.org/10.35634/vm230111 (Mi vuu842) 		 
MATHEMATICS

Integration of the Korteweg-de Vries equation with loaded terms and a self-consistent source in the class of rapidly decreasing functions

U.A. Hoitmetov, T. G. Hasanov

Urgench State University, ul. H. Alimdjan, 14, Urgench, 220100, Uzbekistan
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DOI: https://doi.org/10.35634/vm230111
Abstract: In this paper, we solve the Cauchy problem for the Korteweg-de Vries equation with loaded terms and a self-consistent source in the class of rapidly decreasing functions. To solve this problem, the method of the inverse scattering problem is used. The evolution of the scattering data of the self-adjoint Sturm-Liouville operator, whose coefficient is a solution of the Korteweg-de Vries equation with loaded terms and a self-consistent source, is obtained. Examples are given to illustrate the application of the obtained results.
Keywords: loaded Korteweg-de Vries equation, Jost solutions, inverse scattering problem, Gelfand-Levitan-Marchenko integral equation, evolution of the scattering data.
Received: 06.10.2022
Accepted: 26.12.2022
Bibliographic databases:
Document Type: Article
UDC: 517.956
MSC: 34L25, 35P25, 47A40, 37K15
Language: English
Citation: U.A. Hoitmetov, T. G. Hasanov, “Integration of the Korteweg-de Vries equation with loaded terms and a self-consistent source in the class of rapidly decreasing functions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 33:1 (2023), 156–170
Citation in format AMSBIB
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\by U.A.~Hoitmetov, T.~G.~Hasanov
\paper Integration of the Korteweg-de Vries equation with loaded terms and a self-consistent source in the class of rapidly decreasing functions
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2023
\vol 33
\issue 1
\pages 156--170
\mathnet{http://mi.mathnet.ru/vuu842}
\crossref{https://doi.org/10.35634/vm230111}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4573575}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=001101545900011}
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    		Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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