New optical solitons and modulation instability analysis of generalized coupled nonlinear Schrödinger–KdV system

In this study, the generalized coupled nonlinear Schrödinger–KdV (NLS–KdV) system is investigated to obtain new optical soliton solutions. This appears as a model for reciprocity between long and short waves in various physical settings. Different kinds of solutions including dark, bright, combined dark-bright, singular are obtained using two effective methods namely, extended sinh–Gordon equation expansion method solitary wave ansatz method. addition, modulation instability analysis presented based on standard linear-stability analysis. The behaviours expressed by 3D graphs.