Abstract:
In the article we apply the inverse scattering method to integrating the loaded Korteweg-de Vries equation with a self-consistent source of integral type in the class of rapidly decreasing complex-valued functions.
Key words:
loaded Korteweg-de Vries equation, Sturm–Liouville operator, Jost solutions, scattering data, inverse problem of scattering theory, Gelfand–Levitan–Marchenko integral equation.
Citation:
U. A. Hoitmetov, “Integrating the loaded KdV equation with a self-consistent source of integral type in the class of rapidly decreasing complex-valued functions”, Mat. Tr., 24:2 (2021), 181–198
\Bibitem{Hoi21}
\by U.~A.~Hoitmetov
\paper Integrating the loaded KdV equation with a~self-consistent source of integral type in the class of rapidly decreasing complex-valued functions
\jour Mat. Tr.
\yr 2021
\vol 24
\issue 2
\pages 181--198
\mathnet{http://mi.mathnet.ru/mt657}
\crossref{https://doi.org/10.33048/mattrudy.2021.24.211}
Linking options:
https://www.mathnet.ru/eng/mt657
https://www.mathnet.ru/eng/mt/v24/i2/p181
This publication is cited in the following 2 articles:
U. A. Khoitmetov, “Integration of the Hirota equation with time-dependent coefficients”, Theoret. and Math. Phys., 214:1 (2023), 24–35
U.A. Hoitmetov, T. G. Hasanov, “Integration of the Korteweg-de Vries equation with loaded terms and a self-consistent source in the class of rapidly decreasing functions”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 33:1 (2023), 156–170
Citation in format AMSBIB
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