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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2024, Volume 63, Pages 80–90
DOI: https://doi.org/10.35634/2226-3594-2024-63-06 (Mi iimi463) 		 
MATHEMATICS

Integration of negative-order modified Korteweg–de Vries equation with an integral source

G. U. Urazboeva, M. M. Khasanova, O. B. Ismoilovb

a Urgench State University, ul. Kh. Alimdjan, 14, Urgench, 220100, Uzbekistan
b V. I. Romanovskiy Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Khorezm branch, ul. Kh. Alimdjan, 14, Urgench, 220100, Uzbekistan
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DOI: https://doi.org/10.35634/2226-3594-2024-63-06
Abstract: In this paper, it is shown that the modified Korteweg–de Vries (mKdV) equation of negative order with an integral source can be integrated by the method of the inverse spectral problem. The main result of this work is the derivation of the evolution of the spectral data of the Dirac system with a periodic potential associated with the solution of the negative-order modified Korteweg–de Vries equation with an integral source. The obtained results allow us to apply the inverse problem method to solve the negative-order modified Korteweg–de Vries equation with an integral source.
Keywords: modified Korteweg–de Vries equation of negative order, Dirac system, inverse spectral problem, Dubrovin–Trubowitz system of equations, trace formulas
Received: 15.04.2024
Accepted: 10.05.2024
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: 35P25, 35P30, 35Q51, 35Q53, 37K15
Language: Russian
Citation: G. U. Urazboev, M. M. Khasanov, O. B. Ismoilov, “Integration of negative-order modified Korteweg–de Vries equation with an integral source”, Izv. IMI UdGU, 63 (2024), 80–90
Citation in format AMSBIB
\Bibitem{UraKhaIsm24}
\by G.~U.~Urazboev, M.~M.~Khasanov, O.~B.~Ismoilov
\paper Integration of negative-order modified Korteweg–de Vries equation with an integral source
\jour Izv. IMI UdGU
\yr 2024
\vol 63
\pages 80--90
\mathnet{http://mi.mathnet.ru/iimi463}
\crossref{https://doi.org/10.35634/2226-3594-2024-63-06}
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