A. B. Khasanov, U. A. Khoitmetov, “On integration of Korteweg–de Vries equation in a class of rapidly decreasing complex-valued functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 3,Pages <nobr>79

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On integration of Korteweg–de Vries equation in a class of rapidly decreasing complex-valued functions

A. B. Khasanov^a, U. A. Khoitmetov^b

^a Urgench State University, 14 Alimdzhana str., Urgench, 220100 Republic of Uzbekistan
^b Urgench Branch of Tashkent University of Informational Technologies, 110 Al-Khorezmi str., Urgench, 220100 Republic of Uzbekistan

Abstract: We apply the inverse scattering method to the integration of the Korteweg-de Vries equation with self-consistent source in the class of complex-valued rapidly decreasing functions.

Keywords: Korteweg-de Vries equation, Sturm–Liouville operator, Jost solutions, inverse scattering problem, Gelfand–Levitan–Marchenko integral equation.

UDC: 517.956

Received: 12.12.2016