(untitled) (Journal of Science-Innovative Research in Uzbekistan, 2023)
The theory of inverse scattering is studied to solve the initial-value problem for the nonlinear Schrodinger equation with a self-consistent source and the finite density type initial data. In direct scattering problem, we establish the Jost eigenfunctions, scattering data and their analyticity and symmetry. Moreover, the asymptotic behavior of the Jost functions of the Dirac’s type operator and scattering data are analyzed needed in inverse problem