In this study the generalized exponential rational function approach is used to extract some new exact solitary wave solutions of the generalized coupled nonlinear Schrödinger–Korteweg–de Vries equations. These coupled equations appear in interactions between short and long dispersive waves which are important in a variety of applied sciences and engineering domains. With the help of the Mathematica package software, the solutions found in this study were verified. We also show graphical representations of the solutions for a better understanding of the coupled equations’ behavior and physical structures.