Geodesic
Integration of the general loaded Korteweg--de Vries equation with an integral type source in the class of rapidly decreasing complex-valued functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2021), pp. 52-66

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In this paper, the evolution of the scattering data of the Sturm-Liouville operator is derived by the method of the inverse scattering problem, the potential of which is a solution to the general loaded Korteweg-de Vries equation in the class of rapidly decreasing complex-valued functions.
Keywords: Korteweg-de Vries equation, Sturm-Liouville operator, inverse scattering theory, Gelfand-Levitan-Marchenko integral equation.
Mots-clés : Jost solution 
@article{IVM_2021_7_a5,
     author = {A. B. Khasanov and U. A. Hoitmetov},
     title = {Integration of the general loaded {Korteweg--de} {Vries} equation with an integral type source in the class of rapidly decreasing complex-valued functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {52--66},
     publisher = {mathdoc},
     number = {7},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_7_a5/}
}
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A. B. Khasanov; U. A. Hoitmetov. Integration of the general loaded Korteweg--de Vries equation with an integral type source in the class of rapidly decreasing complex-valued functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2021), pp. 52-66. http://geodesic.mathdoc.fr/item/IVM_2021_7_a5/