Integration of the General Loaded Korteweg–de Vries Equation with an Integral Type Source in the Class of Rapidly Decreasing Complex-Valued Functions

In this paper, the evolution of the scattering data of the Sturm–Liouville operator is derived by the method of the inverse scattering problem, here the potential of operator is a solution to the general loaded Korteweg–de Vries equation in the class of rapidly decreasing complex-valued functions....

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Bibliographic Details
Published inRussian mathematics Vol. 65; no. 7; pp. 43 - 57
Main Authors Khasanov, A. B., Hoitmetov, U. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.07.2021
Springer Nature B.V
Subjects
Inverse scattering
Korteweg-Devries equation
Mathematics
Mathematics and Statistics
Operators (mathematics)
Gelfand–Levitan–Marchenko integral equation
Sturm–Liouville operator
Jost solution
inverse problem of scattering theory
Korteweg–de Vries equation
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Summary:In this paper, the evolution of the scattering data of the Sturm–Liouville operator is derived by the method of the inverse scattering problem, here the potential of operator is a solution to the general loaded Korteweg–de Vries equation in the class of rapidly decreasing complex-valued functions.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X21070069