Degenerate solitons in a generalized nonlinear Schrödinger equation

Today, nonlinear Schrödinger-type equations are the focus of explorers and scientists. Hereby, we look into a generalized nonlinear Schrödinger equation by constructing the modified generalized Darboux transformation and analysing the type-I, type-II and type-III degenerate solitons for generalized nonlinear Schrödinger equation via some semirational solutions. Type-I degenerate solitons refer to the degenerate solitons, type-II degenerate solitons mean the interactions between the solitons and the degenerate solitons, and type-III degenerate solitons denote the bound states among a series of the degenerate solitons. We hope that the mathematical research method used in this paper could provide some theoretical assistance for future research on the nonlinear Schrödinger-type equations.