Abstract
The higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms is studied in this work. The pulses propagation beyond ultra-short range in the systems of optical communication is described through this dynamical model. The modified extended direct algebraic technique is utilized for deriving different kinds exact solutions such as bright–dark solitons, kink and anti-kink solitons, solitary waves, periodic solutions and elliptic function solutions of this dynamical model. These achieved exact solutions are more general and are useful to researcher for understanding physical phenomena. The structures of some solutions at suitable values of parameters are presented and helpful for knowing the physical interpretation. Several solutions are novel by comparing these solutions with existing solutions. The power and effectiveness of current can observed form constructed solutions.