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Teoreticheskaya i Matematicheskaya Fizika, 2023, Volume 216, Number 1, Pages 63–75
DOI: https://doi.org/10.4213/tmf10482 (Mi tmf10482) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Integration of the Kaup–Boussinesq system with time-dependent coefficients

B. A. Babajanovab, A. Sh. Azamatova, R. B. Atajanovaa

a Urgench State University, Urgench, Uzbekistan
b Romanovsky Institute of Mathematics, Khorezm Branch of the Academy of Sciences of Uzbekistan, Urgench, Uzbekistan
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DOI: https://doi.org/10.4213/tmf10482
Abstract: We consider the Kaup–Boussinesq system with time-dependent coefficients. We show that the Kaup–Boussinesq system with an additional term is also an important theoretical model, since it is a completely integrable system. We find the time evolution of scattering data for a quadratic pencil of Sturm–Liouville operators associated with the solution of the Kaup–Boussinesq system with time-dependent coefficients. The resulting equalities completely determine the scattering data at any $t$, which allows using the inverse scattering method for solving the Cauchy problem for the Kaup–Boussinesq system with time-dependent coefficients. An example is given to illustrate the application of the obtained results.
Keywords: Kaup–Boussinesq system, quadratic pencil of Sturm–Liouville operators, inverse scattering method, soliton solution.
Received: 15.02.2023
Revised: 15.02.2023
English version:
Theoretical and Mathematical Physics, 2023, Volume 216, Issue 1, Pages 961–972
DOI: https://doi.org/10.1134/S004057792307005X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: B. A. Babajanov, A. Sh. Azamatov, R. B. Atajanova, “Integration of the Kaup–Boussinesq system with time-dependent coefficients”, TMF, 216:1 (2023), 63–75; Theoret. and Math. Phys., 216:1 (2023), 961–972
Citation in format AMSBIB
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\by B.~A.~Babajanov, A.~Sh.~Azamatov, R.~B.~Atajanova
\paper Integration of the~Kaup--Boussinesq system with time-dependent coefficients
\jour TMF
\yr 2023
\vol 216
\issue 1
\pages 63--75
\mathnet{http://mi.mathnet.ru/tmf10482}
\crossref{https://doi.org/10.4213/tmf10482}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4619867}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2023TMP...216..961B}
\transl
\jour Theoret. and Math. Phys.
\yr 2023
\vol 216
\issue 1
\pages 961--972
\crossref{https://doi.org/10.1134/S004057792307005X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85165608114}
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    • This publication is cited in the following 2 articles:
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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