This article is cited in 1 paper

Scattering theory for the loaded negative order Korteweg–de Vries equation

G. U. Urazboev^ab, I. I. Baltaeva^a, O. B. Ismoilov<sup>b

a</sup> Urgench State University (Urgench, Uzbekistan)
^b V. I. Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan (Khorezm Branch) (Urgench, Uzbekistan)

Abstract: In this paper, we consider the loaded negative order Korteweg–de Vries equation. The evolution of the spectral data of the Sturm–Liouville operator with a potential associated with the solution of the loaded negative order Korteweg–de Vries equation is determined. The obtained results make it possible to apply the inverse problem method to solve the loaded negative order Korteweg–de Vries equation in the class of rapidly decreasing functions. An example of the given problem is given with graphs of the solution.

Keywords: Sturm–Liouville operator, loaded equation, loaded negative order Korteweg–de Vries equation, soliton solution, inverse scattering problems.

UDC: 517.946

Received: 21.03.2024
Accepted: 28.06.2024

Language: English

DOI: 10.22405/2226-8383-2024-25-2-169-180