Integration of the Loaded Cordeveg-De Fries Equation in a Class of Fast Decreasing Functions

Abstract

Annotation: This article is devoted to the integration of the loaded source Korteweg-de Vries equation in the class of rapidly decreasing functions. In this work, the Cauchy problem imposed on the Korteweg-de Vries equation was solved using the inverse problem method of the Sturm-Liouville operator scattering theory. Their Yost solutions are defined and integral Levin images are obtained for them. The givens of the scattering theory were described and some of their necessary properties were given, the Gelfand-Levitan-Marchenko integral equation, which is the main integral equation of the inverse problems of the scattering theory, was derived.

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Identifiers

DOI

10.22214/ijraset.2022.45627

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