N-soliton solutions of the generalized mixed nonlinear Schrodinger equation through the Riemann-Hilbert method

The generalized mixed nonlinear Schrodinger equation is the core of this thesis study and it plays a pivotal position in many physical applications. In this paper, on the whole, in the framework of the Riemann-Hilbert approach, by analyzing the spectral problem of the Lax pair and applying the transformation of the matrix, the Riemann-Hilbert problem of the generalized mixed nonlinear Schrodinger equation for specific values of the parameters is constructed. After that, in the case of irregularity, the N-soliton solutions of this equation at specific values of the parameters can be presented by the scattering transformation. In particular, some three-dimensional images of this nonlinear system can be graphically depicted.