The Darboux Transformation and N-Soliton Solutions of Coupled Cubic-Quintic Nonlinear Schrodinger Equation on a Time-Space Scale

The coupled cubic-quintic nonlinear Schrodinger (CQNLS) equation is a universal mathematical model describing many physical situations, such as nonlinear optics and Bose-Einstein condensate. In this paper, in order to simplify the process of similar analysis with different forms of the coupled CQNLS equation, this dynamic system is extended to a time-space scale based on the Lax pair and zero curvature equation. Furthermore, Darboux transformation of the coupled CQNLS dynamic system on a time-space scale is constructed, and the N-soliton solution is obtained. These results effectively combine the theory of differential equations with difference equations and become a bridge connecting continuous and discrete analysis.