In this paper, new dark and singular solutions are constructed for the generalized nonlinear Schrödinger equation with higher order dispersion and cubic-quintic nonlinear terms using a relatively new technique, namely the generalized exponential rational function method (GERFM). Moreover, the modulation instability analysis (MIA) of the underlying equation is studied by using linear-stability analysis and the gain spectrum in the modulation instability is computed. Numerical simulations are made to shed light on characteristics of the obtained solutions
