Open AccessIntegration of the Harry Dym equation with an integral type source
Author(s) -
G. U. Urazboev,
A. K. Babadjanova,
D.R. Saparbaeva
Publication year - 2021
Publication title -
vestnik udmurtskogo universiteta. matematika, mehanika, kompʹûternye nauki
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 8
eISSN - 2076-5959
pISSN - 1994-9197
DOI - 10.35634/vm210209
Subject(s) - integral equation , inverse scattering problem , type (biology) , inverse scattering transform , scattering , mathematics , cauchy distribution , mathematical analysis , inverse problem , initial value problem , physics , optics , geology , paleontology
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.