Geodesic
On integration of the loaded mKdV equation in the class of rapidly decreasing functions
The Bulletin of Irkutsk State University. Series Mathematics, Tome 38 (2021), pp. 19-35

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The paper is devoted to the integration of the loaded modified Korteweg-de Vries equation in the class of rapidly decreasing functions. It is well known that loaded differential equations in the literature are usually called equations containing in the coefficients or in the right-hand side any functionals of the solution, in particular, the values of the solution or its derivatives on manifolds of lower dimension. In this paper, we consider the Cauchy problem for the loaded modified Korteweg-de Vries equation. The problem is solved using the inverse scattering method, i.e. the evolution of the scattering data of a non-self-adjoint Dirac operator is derived, the potential of which is a solution to the loaded modified Korteweg-de Vries equation in the class of rapidly decreasing functions. A specific example is given to illustrate the application of the results obtained.
Keywords: loaded modified Korteweg-de Vries equation, inverse scattering problem, Gelfand-Levitan-Marchenko integral equation, evolution of scattering data.
Mots-clés : Jost solutions 
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     author = {A. B. Khasanov and U. A. Hoitmetov},
     title = {On integration of the loaded {mKdV} equation in the class of rapidly decreasing functions},
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     volume = {38},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2021_38_a1/}
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A. B. Khasanov; U. A. Hoitmetov. On integration of the loaded mKdV equation in the class of rapidly decreasing functions. The Bulletin of Irkutsk State University. Series Mathematics, Tome 38 (2021), pp. 19-35. http://geodesic.mathdoc.fr/item/IIGUM_2021_38_a1/