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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2023, Volume 61, Pages 137–155
DOI: https://doi.org/10.35634/2226-3594-2023-61-08 (Mi iimi446) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Integration of the mKdV Equation with nonstationary coefficients and additional terms in the case of moving eigenvalues

A. B. Khasanova, U.A. Hoitmetovb, Sh. Q. Sobirovb

a Samarkand State University, University boulvard, 15, Samarkand, 140104, Uzbekistan
b Urgench State University, ul. Khamida Alimdjana, 14, Urgench, 220100, Uzbekistan
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DOI: https://doi.org/10.35634/2226-3594-2023-61-08
Abstract: In this paper, we consider the Cauchy problem for the non-stationary modified Korteweg–de Vries equation with an additional term and a self-consistent source in the case of moving eigenvalues. Also, the evolution of the scattering data of the Dirac operator is obtained, the potential of which is the solution of the loaded modified Korteweg–de Vries equation with a self-consistent source in the class of rapidly decreasing functions. Specific examples are given to illustrate the application of the obtained results.
Keywords: Gelfand–Levitan–Marchenko integral equation, system of Dirac equations, Jost solutions, scattering data.
Received: 30.12.2022
Accepted: 17.04.2023
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: 37K15
Language: English
Citation: A. B. Khasanov, U.A. Hoitmetov, Sh. Q. Sobirov, “Integration of the mKdV Equation with nonstationary coefficients and additional terms in the case of moving eigenvalues”, Izv. IMI UdGU, 61 (2023), 137–155
Citation in format AMSBIB
\Bibitem{KhaHoiSob23}
\by A.~B.~Khasanov, U.A.~Hoitmetov, Sh.~Q.~Sobirov
\paper Integration of the mKdV Equation with nonstationary coefficients and additional terms in the case of moving eigenvalues
\jour Izv. IMI UdGU
\yr 2023
\vol 61
\pages 137--155
\mathnet{http://mi.mathnet.ru/iimi446}
\crossref{https://doi.org/10.35634/2226-3594-2023-61-08}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=001005574800008}
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    • This publication is cited in the following 1 articles:
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    		Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
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