Abstract:
In this paper, the possibility of using the inverse scattering problem method to integrate the mKdV equation with a self-consistent source in the class of finite density functions in the case of moving simple eigenvalues of the corresponding spectral problem is shown.
Keywords:
inverse scattering problem method, modified Korteweg-de Vries equation (mKdV), Dirac operator, Jost solution, eigenvalue, eigenfunction, scattering data, class of functions having finite density.
Citation:
K. A. Mamedov, “Integration of mKdV equation with a self-consistent source in the class of finite density functions in the case of moving eigenvalues”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 10, 73–85; Russian Math. (Iz. VUZ), 64:10 (2020), 66–78
\Bibitem{Mam20}
\by K.~A.~Mamedov
\paper Integration of mKdV equation with a self-consistent source in the class of finite density functions in the case of moving eigenvalues
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2020
\issue 10
\pages 73--85
\mathnet{http://mi.mathnet.ru/ivm9620}
\crossref{https://doi.org/10.26907/0021-3446-2020-10-73-85}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2020
\vol 64
\issue 10
\pages 66--78
\crossref{https://doi.org/10.3103/S1066369X20100072}
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Linking options:
https://www.mathnet.ru/eng/ivm9620
https://www.mathnet.ru/eng/ivm/y2020/i10/p73
This publication is cited in the following 9 articles:
G.U. Urazboev, I.I. Baltaeva, Sh.E. Atanazarova, “Analysis of the solitary wave solutions of the negative order modified Korteweg –de Vries equation with a self-consistent source”, Partial Differential Equations in Applied Mathematics, 2025, 101108
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
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
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
G. U. Urazboev, A. B. Yakhshimuratov, M. M. Khasanov, “Integration of negative-order modified Korteweg–de Vries equation in a class of periodic functions”, Theoret. and Math. Phys., 217:2 (2023), 1689–1699
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
U. B. Muminov, A. B. Khasanov, “Zadacha Koshi dlya defokusiruyuschego nelineinogo uravneniya Shredingera s nagruzhennym chlenom”, Matem. tr., 25:1 (2022), 102–133
U. B. Muminov, A. B. Khasanov, “The Cauchy Problem for the Defocusing Nonlinear Schrödinger Equation with a Loaded Term”, Sib. Adv. Math., 32:4 (2022), 277
A. B. Khasanov, U. A. Hoitmetov, “On integration of the loaded mKdV equation in the class of rapidly decreasing functions”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 38 (2021), 19–35
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