This article is cited in 10 papers

MATHEMATICS

Integration of the negative order Korteweg–de Vries equation by the inverse scattering method

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

a</sup> Urgench State University, ul. H. Alimdjan, 14, Urgench, 220100, Uzbekistan
^b V. I. Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, Khorezm Branch, ul. H. Alimdjan, 14, Urgench, 220100, Uzbekistan

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

Keywords: Sturm-Liouville operator, negative order Korteweg-de Vries equation, scattering data, inverse scattering problem.

UDC: 517.958

MSC: 34L25, 35C08, 35P25, 35Q51, 35Q53

Received: 19.05.2023
Accepted: 22.08.2023

DOI: 10.35634/vm230309

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