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Integration of the negative order Korteweg-de Vries equation with self-consistent source

Mičhal FĕckanComenius University in Bratislava, Bratislava, SlovakiaG. U. UrazboevUrgench State University, Khorezm, Uzbekistan; V.I.Romanovsky Institute of Mathematics of the Academy of Sciences of Uzbekistan, Khorezm branch, Khorezm, UzbekistanIroda Ismailovna BaltaevaUrgench State University, Khorezm, UzbekistanO. B. IsmoilovV.I.Romanovsky Institute of Mathematics of the Academy of Sciences of Uzbekistan, Khorezm branch, Khorezm, Uzbekistan; Urgench State University, Khorezm, Uzbekistan
2023en
ABI

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In this paper, we show that the negative-order Korteweg-de Vries equation with a self-consistent source can be solved by the inverse scattering method. The evolution of the spectral data of the Sturm-Liouville operator with the potential associated with the solution of the negative order Korteweg-de Vries equation with a self-consistent source is determined. The results obtained make it possible to apply the method of the inverse scattering problem to solve the problem under consideration.

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