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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, Volume 32, Issue 2, Pages 228–239
DOI: https://doi.org/10.35634/vm220205 (Mi vuu808) 		 
This article is cited in 8 scientific papers (total in 8 papers)

MATHEMATICS

Integration of the negative order Korteweg-de Vries equation with a self-consistent source in the class of periodic functions

G. U. Urazboev, M. M. Hasanov

Urgench State University, ul. Kh. Alimdjan, 14, Urgench, 220100, Uzbekistan
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DOI: https://doi.org/10.35634/vm220205
Abstract: In this paper, we consider the negative order Korteweg–de Vries equation with a self-consistent integral source. It is shown that the negative-order Korteweg–de Vries equation with a self-consistent integral source can be integrated by the method of the inverse spectral problem. The evolution of the spectral data of the Sturm–Liouville operator with a periodic potential associated with the solution of the negative order Korteweg–de Vries equation with a self-consistent integral source is determined. The obtained results make it possible to apply the inverse problem method to solve the negative order Korteweg–de Vries equation with a self-consistent source in the class of periodic functions.
Keywords: negative-order KdV, self-consistent source, inverse spectral problem.
Received: 28.03.2022
Accepted: 28.05.2022
Bibliographic databases:
Document Type: Article
UDC: 517.946
MSC: 35P25, 35P30, 35Q51, 35Q53, 37K15
Language: Russian
Citation: G. U. Urazboev, M. M. Hasanov, “Integration of the negative order Korteweg-de Vries equation with a self-consistent source in the class of periodic functions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 32:2 (2022), 228–239
Citation in format AMSBIB
\Bibitem{UraKha22}
\by G.~U.~Urazboev, M.~M.~Hasanov
\paper Integration of the negative order Korteweg-de Vries equation with a self-consistent source in the class of periodic functions
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2022
\vol 32
\issue 2
\pages 228--239
\mathnet{http://mi.mathnet.ru/vuu808}
\crossref{https://doi.org/10.35634/vm220205}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4456917}
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    • This publication is cited in the following 8 articles:
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