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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 2, Pages 859–879
DOI: https://doi.org/doi.org/10.33048/semi.2023.20.053 (Mi semr1616) 		 
Differentical equations, dynamical systems and optimal control

Integration of the loaded mKdV-sine-Gordon equation with a source

U. A. Hoitmetov

Urgench Stete University, Kh. Alimdjan str., 14, 220100, Urgench, Uzbekistan
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DOI: https://doi.org/doi.org/10.33048/semi.2023.20.053
Abstract: The work is devoted to finding the solution of the Cauchy problem for the loaded modified Korteweg-de Vries–sine-Gordon (mKdV-sG) equation with a source in the class of rapidly decreasing functions. The problem is solved by the inverse scattering method. Several examples are given illustrating the application of the obtained results.
Keywords: loaded mKdV–sine-Gordon equation, Jost solutions, inverse scattering problem, Gelfand-Levitan-Marchenko integral equation, evolution of the scattering data.
Received March 22, 2022, published November 7, 2023
Document Type: Article
UDC: 517.957
MSC: 37K15
Language: English
Citation: U. A. Hoitmetov, “Integration of the loaded mKdV-sine-Gordon equation with a source”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 859–879
Citation in format AMSBIB
\Bibitem{Hoi23}
\by U.~A.~Hoitmetov
\paper Integration of the loaded mKdV-sine-Gordon equation with a source
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 2
\pages 859--879
\mathnet{http://mi.mathnet.ru/semr1616}
\crossref{https://doi.org/doi.org/10.33048/semi.2023.20.053}
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