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JOURNALS // Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki // Archive

Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2023 Volume 33, Issue 1, Pages 156–170 (Mi vuu842)

MATHEMATICS

Integration of the Korteweg-de Vries equation with loaded terms and a self-consistent source in the class of rapidly decreasing functions

U.A. Hoitmetov, T. G. Hasanov

Urgench State University, ul. H. Alimdjan, 14, Urgench, 220100, Uzbekistan

Abstract: In this paper, we solve the Cauchy problem for the Korteweg-de Vries equation with loaded terms and a self-consistent source in the class of rapidly decreasing functions. To solve this problem, the method of the inverse scattering problem is used. The evolution of the scattering data of the self-adjoint Sturm-Liouville operator, whose coefficient is a solution of the Korteweg-de Vries equation with loaded terms and a self-consistent source, is obtained. Examples are given to illustrate the application of the obtained results.

Keywords: loaded Korteweg-de Vries equation, Jost solutions, inverse scattering problem, Gelfand-Levitan-Marchenko integral equation, evolution of the scattering data.

UDC: 517.956

MSC: 34L25, 35P25, 47A40, 37K15

Received: 06.10.2022
Accepted: 26.12.2022

Language: English

DOI: 10.35634/vm230111



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© Steklov Math. Inst. of RAS, 2024