Geodesic
Integration of the Korteweg-de Vries equation with loaded terms and a self-consistent source in the class of rapidly decreasing functions
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 1, pp. 156-170 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we solve the Cauchy problem for the Korteweg-de Vries equation with loaded terms and a self-consistent source in the class of rapidly decreasing functions. To solve this problem, the method of the inverse scattering problem is used. The evolution of the scattering data of the self-adjoint Sturm-Liouville operator, whose coefficient is a solution of the Korteweg-de Vries equation with loaded terms and a self-consistent source, is obtained. Examples are given to illustrate the application of the obtained results.
Keywords: loaded Korteweg-de Vries equation, inverse scattering problem, Gelfand-Levitan-Marchenko integral equation, evolution of the scattering data.
Mots-clés : Jost solutions 
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     title = {Integration of the {Korteweg-de} {Vries} equation with loaded terms and a self-consistent source in the class of rapidly decreasing functions},
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U.A. Hoitmetov; T. G. Hasanov. Integration of the Korteweg-de Vries equation with loaded terms and a self-consistent source in the class of rapidly decreasing functions. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 1, pp. 156-170. http://geodesic.mathdoc.fr/item/VUU_2023_33_1_a10/

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