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Chebyshevskii Sbornik, 2023, Volume 24, Issue 2, Pages 266–275
DOI: https://doi.org/10.22405/2226-8383-2023-24-2-266-275 (Mi cheb1319) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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Integration of the KdV equation of negative order with a free term in the class of periodic functions

M. M. Khasanov, I. D. Rakhimov

Urganch State University (Urganch)
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DOI: https://doi.org/10.22405/2226-8383-2023-24-2-266-275
Abstract: In this paper, we consider the KdV equation of negative order with a free term in the class of periodic functions. It is shown that the KdV equation of negative order with a free term in the class of periodic functions 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 a negative-order KdV equation with a free term in the class of periodic functions is determined. The results obtained make it possible to apply the inverse problem method to the solution of the KdV equation of negative order with a free term in the class of periodic functions.
Keywords: KdV of negative order, self-consistent source, inverse spectral problem, Dubrovin–Trubovits system of equations.
Received: 13.02.2023
Accepted: 14.06.2023
Document Type: Article
UDC: 517.946
Language: Russian
Citation: M. M. Khasanov, I. D. Rakhimov, “Integration of the KdV equation of negative order with a free term in the class of periodic functions”, Chebyshevskii Sb., 24:2 (2023), 266–275
Citation in format AMSBIB
\Bibitem{KhaRak23}
\by M.~M.~Khasanov, I.~D.~Rakhimov
\paper Integration of the KdV equation of negative order with a free term in the class of periodic functions
\jour Chebyshevskii Sb.
\yr 2023
\vol 24
\issue 2
\pages 266--275
\mathnet{http://mi.mathnet.ru/cheb1319}
\crossref{https://doi.org/10.22405/2226-8383-2023-24-2-266-275}
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    • This publication is cited in the following 2 articles:
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