This article is cited in 2 papers

Inverse scattering and loaded modified Korteweg-de Vries equation

Michal Fečkan^a, Gayrat Urazboev^bc, Iroda Baltaeva<sup>db

a</sup> Mathematical Institute of the Slovak Academy of Sciences Bratislava, Slovakia
^b Urgench state university, Urgench, Uzbekistan
^c Institute of Mathematics, Khorezm Branch, Uzbekistan Academy of Sciences, Urgench, Uzbekistan
^d Khorezm Mamun Academy, Khorezm region, Khiva, Uzbekistan

Abstract: The Cauchy problem for the loaded modified Korteweg-de Vries equation in the class of "rapidly decreasing" functions is considered in this paper. The main result of this work is a theorem on the evolution of the scattering data of the Dirac operator. Potential of the operator is the solution to the loaded modified Korteweg-de Vries equation. The obtained equalities allow one to apply the method of the inverse scattering transform to solve the Cauchy problem for the loaded modified Korteweg-de Vries equation.

Keywords: loaded modified KdV equation, inverse scattering method, "rapidly decreasing" functions, soliton, evolution of the scattering data.

UDC: 517.95

Received: 11.09.2021
Received in revised form: 19.11.2021
Accepted: 10.02.2022

Language: English

DOI: 10.17516/1997-1397-2022-15-2-176-185