Section
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Mathematics
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Title
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Integration of the Harry Dym equation with an integral type source
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Author(-s)
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Urazboev G.U.ab,
Babadjanova A.K.a,
Saparbaeva D.R.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 the work, we deduce the evolution of scattering data for a spectral problem associated with the nonlinear evolutionary equation of Harry Dym with a self-consistent source of integral type. 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 Harry Dym equation with an integral type source.
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Keywords
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nonlinear evolution equation, Harry Dym equation, integral source, inverse scattering method, Gelfand–Levitan–Marchenko equation
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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/vm210209
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Received
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24 December 2020
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Language
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English
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Citation
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Urazboev G.U., Babadjanova A.K., Saparbaeva D.R. Integration of the Harry Dym equation with an integral type source, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 2, pp. 285-295.
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