Geodesic
Inverse scattering and loaded modified Korteweg-de Vries equation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 176-185

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The Cauchy problem for the loaded modified Korteweg-de Vries equation in the class of "rapidly decreasing" functions is considered in this paper. The main result of this work is a theorem on the evolution of the scattering data of the Dirac operator. Potential of the operator is the solution to the loaded modified Korteweg-de Vries equation. The obtained equalities allow one to apply the method of the inverse scattering transform to solve the Cauchy problem for the loaded modified Korteweg-de Vries equation.
Keywords: loaded modified KdV equation, inverse scattering method, "rapidly decreasing" functions, evolution of the scattering data.
Mots-clés : soliton 
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     author = {Michal Fe\v{c}kan and Gayrat Urazboev and Iroda Baltaeva},
     title = {Inverse scattering and loaded modified {Korteweg-de} {Vries} equation},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     publisher = {mathdoc},
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     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a3/}
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Michal Fečkan; Gayrat Urazboev; Iroda Baltaeva. Inverse scattering and loaded modified Korteweg-de Vries equation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 176-185. http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a3/