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## Archive of Issues

Uzbekistan Urgench
Year
2022
Volume
32
Issue
2
Pages
228-239
 Section Mathematics Title Integration of the negative order Korteweg–de Vries equation with a self-consistent source in the class of periodic functions Author(-s) Urazboev G.U.a, Hasanov M.M.a Affiliations Urgench State Universitya Abstract In this paper, we consider the negative order Korteweg–de Vries equation with a self-consistent integral source. It is shown that the negative-order Korteweg–de Vries equation with a self-consistent integral source can be integrated by the method of the inverse spectral problem. The evolution of the spectral data of the Sturm–Liouville operator with a periodic potential associated with the solution of the negative order Korteweg–de Vries equation with a self-consistent integral source is determined. The obtained results make it possible to apply the inverse problem method to solve the negative order Korteweg–de Vries equation with a self-consistent source in the class of periodic functions. 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