Abstract:
In this paper, the evolution of the scattering data of the Sturm-Liouville operator is derived
by the method of the inverse scattering problem, the potential of which is a solution to the loaded general
Korteweg-de Vries equation in the class of rapidly decreasing complex-valued functions.
Keywords and phrases:
loaded general Korteweg-de Vries equation, Sturm-Liouville operator, Jost solutions, scattering
data, Gelfand-Levitan-Marchenko integral equation.
Citation:
U. A. Hoitmetov, “Integration of the loaded general Korteweg-de Vries equation in tne class of rapidly decreasing complex-valued functions”, Eurasian Math. J., 13:2 (2022), 43–54
\Bibitem{Hoi22}
\by U.~A.~Hoitmetov
\paper Integration of the loaded general Korteweg-de Vries equation in tne class of rapidly decreasing complex-valued functions
\jour Eurasian Math. J.
\yr 2022
\vol 13
\issue 2
\pages 43--54
\mathnet{http://mi.mathnet.ru/emj437}
\crossref{https://doi.org/10.32523/2077-9879-2022-13-2-43-54}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4459174}
Linking options:
https://www.mathnet.ru/eng/emj437
https://www.mathnet.ru/eng/emj/v13/i2/p43
This publication is cited in the following 7 articles:
U.A. Khoitmetov, Sh. K. Sobirov, “Integrirovanie uravneniya mKdF s zavisyaschimi ot vremeni koeffitsientami, s dopolnitelnym chlenom i s integralnym istochnikom v klasse bystroubyvayuschikh funktsii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 34:2 (2024), 248–266
B.A. Babajanov, Sh.O. Sadullaev, M.M. Ruzmetov, “Integration of the Kaup–Boussinesq system via inverse scattering method”, Partial Differential Equations in Applied Mathematics, 11 (2024), 100813
Sh. K. Sobirov, U. A. Hoitmetov, “Integration of the Modified Korteweg-de Vries Equation with Time-Dependent Coefficients and a Self-Consistent Source”, Sib Math J, 65:4 (2024), 971
O. S. Balashov, A. V. Faminskii, “On direct and inverse problems for systems of odd-order quasilinear evolution equations”, Eurasian Math. J., 15:4 (2024), 33–53
U. A. Khoitmetov, “Integration of the Hirota equation with time-dependent coefficients”, Theoret. and Math. Phys., 214:1 (2023), 24–35
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
Sh. K. Sobirov, U.A. Khoitmetov, “Integrirovanie modifitsirovannogo uravneniya Kortevega — de Friza s zavisyaschimi ot vremeni koeffitsientami i s samosoglasovannym istochnikom”, Vladikavk. matem. zhurn., 25:3 (2023), 123–142
Citation in format AMSBIB
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