Generalized (n,N − n)-fold Darboux transformation and localized wave solutions for a general coupled nonlinear Schrödinger equations

Here, using a generalized $(n,N-n)$-fold Darboux transformation of the general coupled nonlinear Schrödinger equations and categorizing solutions by the number of distinct spectral parameters, we obtain three degenerate solution types in determinant form: (i) degenerate solutions from a single spectral parameter; (ii) hybrid solutions from two distinct spectral parameters; (iii) hybrid solutions from three or more distinct spectral parameters. Notably, it is the solutions (iii) that give rise to a novel semirational solution. Additionally, we study four-wave mixing effects on the localized waves structures and the distinct dynamics of each solution type.