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Uzbekistan Urgench
Section Mathematics
Title Integration of the Harry Dym equation with an integral type source
Author(-s) Urazboev G.U.ab, Babadjanova A.K.a, Saparbaeva D.R.b
Affiliations Institute of Mathematics, Khorezm Branch, Uzbekistan Academy of Sciencesa, Urgench State Universityb
Abstract 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.
Keywords nonlinear evolution equation, Harry Dym equation, integral source, inverse scattering method, Gelfand–Levitan–Marchenko equation
UDC 517.957
MSC 34L25, 35Q41, 37K10, 35R30, 34M46
DOI 10.35634/vm210209
Received 24 December 2020
Language English
Citation 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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