Abstract:
We use the inverse spectral method to integrate a higher-order nonlinear Schrödinger system with a self-consistent source in the class of periodic functions.
Keywords:
Dirac operator, spectral data, nonlinear Schrödinger equation, Dubrovin–Trubowitz system of equations, self-consistent source.
Citation:
A. B. Yakhshimuratov, “Integration of a higher-order nonlinear Schrödinger system with a self-consistent source in the class of periodic functions”, TMF, 202:2 (2020), 157–169; Theoret. and Math. Phys., 202:2 (2020), 137–149
\Bibitem{Yak20}
\by A.~B.~Yakhshimuratov
\paper Integration of a~higher-order nonlinear Schr\"odinger system with a~self-consistent source in the~class of periodic functions
\jour TMF
\yr 2020
\vol 202
\issue 2
\pages 157--169
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\crossref{https://doi.org/10.4213/tmf9712}
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\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2020TMP...202..137Y}
\elib{https://elibrary.ru/item.asp?id=43260543}
\transl
\jour Theoret. and Math. Phys.
\yr 2020
\vol 202
\issue 2
\pages 137--149
\crossref{https://doi.org/10.1134/S0040577920020014}
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Linking options:
https://www.mathnet.ru/eng/tmf9712
https://doi.org/10.4213/tmf9712
https://www.mathnet.ru/eng/tmf/v202/i2/p157
This publication is cited in the following 8 articles:
A. B. Khasanov, R. Kh. Eshbekov, T. G. Hasanov, “Integration of a non-linear Hirota type equation with additional terms”, Izv. Math., 89:1 (2025), 196–219
A. B. Khasanov, T. G. Khasanov, “The Cauchy Problem for the Nonlinear Complex Modified Korteweg-de Vries Equation with Additional Terms in the Class of Periodic Infinite-Gap Functions”, Sib Math J, 65:4 (2024), 846
A. B. Khasanov, T. G. Khasanov, “Zadacha Koshi dlya nelineinogo kompleksnogo modifitsirovannogo uravneniya Kortevega — de Friza (kmKdF) s dopolnitelnymi chlenami v klasse periodicheskikh beskonechnozonnykh funktsii”, Sib. matem. zhurn., 65:4 (2024), 735–759
G. U. Urazboev, M. M. Khasanov, A. K. Babadjanova, “Integration of the Negative Order Nonlinear Schrödinger Equation in the Class of Periodic Functions”, Lobachevskii J Math, 45:10 (2024), 5305
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
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
A. Khasanov, R. Eshbekov, Kh. Normurodov, “Integration of a nonlinear Hirota type equation with finite density in the class of periodic functions”, Lobachevskii J. Math., 44:10 (2023), 4329
G. A. Mannonov, A. B. Khasanov, “The Cauchy problem for a nonlinear Hirota equation in the class of periodic infinite-zone functions”, St. Petersburg Math. J., 34:5 (2023), 821–845
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