Geodesic
Integration of the matrix nonlinear Schrödinger equation with a source
The Bulletin of Irkutsk State University. Series Mathematics, Tome 37 (2021), pp. 63-76 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper is concerned with studying the matrix nonlinear Schrödinger equation with a self-consistent source. The source consists of the combination of the eigenfunctions of the corresponding spectral problem for the matrix Zakharov-Shabat system which has not spectral singularities. The theorem about the evolution of the scattering data of a non-self-adjoint matrix Zakharov-Shabat system which potential is a solution of the matrix nonlinear Schrödinger equation with the self-consistent source is proved. The obtained results allow us to solve the Cauchy problem for the matrix nonlinear Schrödinger equation with a self-consistent source in the class of the rapidly decreasing functions via the inverse scattering method. A one-to-one correspondence between the potential of the matrix Zakharov-Shabat system and scattering data provide the uniqueness of the solution of the considering problem. A step-by-step algorithm for finding a solution to the problem under consideration is presented.
Keywords: matrix nonlinear Schrödinger equation, self-consistent source, inverse scattering method, scattering data. 
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     title = {Integration of the matrix nonlinear {Schr\"odinger} equation with a source},
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     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/IIGUM_2021_37_a4/}
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G. U. Urazboev; A. A. Reyimberganov; A. K. Babadjanova. Integration of the matrix nonlinear Schrödinger equation with a source. The Bulletin of Irkutsk State University. Series Mathematics, Tome 37 (2021), pp. 63-76. http://geodesic.mathdoc.fr/item/IIGUM_2021_37_a4/

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