Integration of the negative order Korteweg–de Vries equation by the inverse scattering method

G. U. Urazboev ; I. I. Baltaeva ; O. B. Ismoilov

Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 3, pp. 523-533

Résumé

In this paper, we consider the integration of the negative order Korteweg-de Vries equation by the inverse scattering method. The evolution of the spectral data of the Sturm-Liouville operator with a potential associated with the solution of the negative order Korteweg-de Vries equation is determined. The obtained results make it possible to apply the method of inverse scattering problem to solve the negative order Korteweg-de Vries equation in the class of rapidly decreasing functions.

Détail

Keywords: Sturm-Liouville operator, negative order Korteweg-de Vries equation, scattering data, inverse scattering problem.

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