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This article is cited in 6 scientific papers (total in 6 papers)
Integro-differential equations and functional analysis
Integration of the negative order Korteweg-de Vries equation with a special source
Gayrat U. Urazboev, Muzaffar M. Khasanov, Iroda I. Baltaeva Urgench State Univeresity, Urgench, Uzbekistan
Abstract:
In this paper, we consider the negative order Korteweg-de Vries equation with a self-consistent source corresponding to the eigenvalues of the corresponding spectral problem. It is shown that the considered equation can be integrated by the method of the inverse spectral problem. The evolution of the spectral data of the Sturm-Liouville operator with a periodic potential associated with the solution of the considered equation is determined. The results obtained make it possible to apply the inverse problem method for solving the negative order Korteweg-de Vries equation with a self-consistent source corresponding to the eigenvalues of the corresponding spectral problem.
Keywords:
negative order Korteweg-de Vries equation, self-consistent source, inverse spectral problem, system of Dubrovin-Trubovitz equations, trace formulas.
Received: 22.10.2022 Revised: 28.02.2023 Accepted: 06.03.2023
Citation:
Gayrat U. Urazboev, Muzaffar M. Khasanov, Iroda I. Baltaeva, “Integration of the negative order Korteweg-de Vries equation with a special source”, Bulletin of Irkutsk State University. Series Mathematics, 44 (2023), 31–43
Linking options:
https://www.mathnet.ru/eng/iigum523 https://www.mathnet.ru/eng/iigum/v44/p31
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