Integration of the negative order Korteweg-de Vries equation with a self-consistent source in the class of periodic functions

G. U. Urazboev   ; M. M. Hasanov

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 32 (2022) no. 2, pp. 228-239

Résumé

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.

Détail

Keywords: negative-order KdV, self-consistent source, inverse spectral problem.

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