Section
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Mathematics
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Title
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Integration of the Kaup–Boussinesq system with a self-consistent source via inverse scattering method
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Author(-s)
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Babajanov B.A.ab,
Azamatov A.Sh.b
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Affiliations
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Institute of Mathematics, Khorezm Branch, Uzbekistan Academy of Sciencesa,
Urgench State Universityb
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Abstract
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In this study we consider the Kaup–Boussinesq system with a self-consistent source. We show that the Kaup–Boussinesq system with a self-consistent source can be integrated by the method of inverse scattering theory. For a solving the problem under consideration, we use the direct and inverse scattering problem of the Sturm–Liouville equation with an energy-dependent potential. The time evolution of the scattering data for the Sturm–Liouville equation with an energy-dependent potentials associated with the solution of the Kaup–Boussinesq system with a self-consistent source is determined. The obtained equalities completely determine the scattering data for any $t$, which makes it possible to apply the method of the inverse scattering problem to solve the Cauchy problem for the Kaup–Boussinesq system with a self-consistent source.
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Keywords
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nonlinear soliton equation, Kaup–Boussinesq system, self-consistent source, inverse scattering method, quadratic pencil of Sturm–Liouville equations
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UDC
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517.957
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MSC
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34L25, 35Q41, 37K10, 35R30, 34M46
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DOI
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10.35634/vm220201
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Received
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11 January 2022
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Language
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English
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Citation
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Babajanov B.A., Azamatov A.Sh. Integration of the Kaup–Boussinesq system with a self-consistent source via inverse scattering method, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, vol. 32, issue 2, pp. 153-170.
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