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

Abstract

The generalized mixed nonlinear Schrödinger 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 Schrödinger equation for specific values of the parameters is constructed. After that, in the case of irregularity, the [Formula: see text]-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.