Geodesic
Integration of the matrix nonlinear Schr\"{o}dinger equation with a source
The Bulletin of Irkutsk State University. Series Mathematics, Tome 37 (2021), pp. 63-76

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IIGUM_2021_37_a4,
     author = {G. U. Urazboev and A. A. Reyimberganov and A. K. Babadjanova},
     title = {Integration of the matrix nonlinear {Schr\"{o}dinger} equation with a source},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {63--76},
     publisher = {mathdoc},
     volume = {37},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2021_37_a4/}
}
TY  - JOUR
AU  - G. U. Urazboev
AU  - A. A. Reyimberganov
AU  - A. K. Babadjanova
TI  - Integration of the matrix nonlinear Schr\"{o}dinger equation with a source
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2021
SP  - 63
EP  - 76
VL  - 37
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2021_37_a4/
LA  - en
ID  - IIGUM_2021_37_a4
ER  - 
%0 Journal Article
%A G. U. Urazboev
%A A. A. Reyimberganov
%A A. K. Babadjanova
%T Integration of the matrix nonlinear Schr\"{o}dinger equation with a source
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2021
%P 63-76
%V 37
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIGUM_2021_37_a4/
%G en
%F IIGUM_2021_37_a4
G. U. Urazboev; A. A. Reyimberganov; A. K. Babadjanova. Integration of the matrix nonlinear Schr\"{o}dinger 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/