Abstract
In this research, we study the generalized Radhakrishnan–Kundu–Lakshmanan equation which describe the dynamics of light pulses and it is also described by the nonlinear Schrödinger family of equations with cubic nonlinear terms. We use two auxiliary equation methods (extended simple equation method and new auxiliary equation method)) to obtain the exact and solitary traveling wave solutions of this model. We get new form of solitary traveling wave solutions for this model which help the researchers who interested in the applications of this model to be able to study the physical properties of the model.