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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 4 scientific papers (total in 4 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
Full-text PDF (453 kB) Citations (4)
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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 tt, 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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  • https://doi.org/10.4213/tmf10482
  • https://www.mathnet.ru/eng/tmf/v216/i1/p63
    • This publication is cited in the following 4 articles:
    1. 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  mathnet  crossref
    2. 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  crossref
    3. B. A. Babajanov, F. B. Abdikarimov, F. U. Sulaymonov, “On the Integration of the Hierarchy of the Kaup–Boussinesq System with a Self-Consistent Source”, Lobachevskii J Math, 45:7 (2024), 3233  crossref
    4. Molahlehi Charles Kakuli, “Application of the generalized double reduction method to the (1+1)-dimensional Kaup–Boussinesq (K–B) system: Exploiting Lie symmetries and conservation laws”, Partial Differential Equations in Applied Mathematics, 12 (2024), 101004  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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