Geodesic
Integration of the loaded mKdV-sine-Gordon equation with a source
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 859-879

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The work is devoted to finding the solution of the Cauchy problem for the loaded modified Korteweg-de Vries–sine-Gordon (mKdV-sG) equation with a source in the class of rapidly decreasing functions. The problem is solved by the inverse scattering method. Several examples are given illustrating the application of the obtained results.
Keywords: loaded mKdV–sine-Gordon 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 loaded {mKdV-sine-Gordon} equation with a source},
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U. A. Hoitmetov. Integration of the loaded mKdV-sine-Gordon equation with a source. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 859-879. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a44/