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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
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
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
Linking options:
https://www.mathnet.ru/eng/tmf10482https://doi.org/10.4213/tmf10482 https://www.mathnet.ru/eng/tmf/v216/i1/p63
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Abstract page: | 106 | Russian version HTML: | 52 | References: | 20 | First page: | 10 |
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