Article

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

U. A. HoitmetovUrgench State UniversityT.G. KhasanovUrgench State University

Vestnik Udmurtskogo Universiteta Matematika Mekhanika Komp yuternye Naukijournal2023en

ABI

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.

Topics

Numerical methods in inverse problems Differential Equations and Boundary Problems Advanced Mathematical Physics Problems

Identifiers

DOI: 10.35634/vm230111

Citations and references

Cited by 032 references

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