In this article, we study the connection between the -expansion method and the exp -expansion method with the aid of a suitable transformation. We employ these two methods to derive families of exact solutions for a higher order dispersive nonlinear Schrödinger equation describing the propagation of the optical pulse in a medium. Comparison between these two methods is presented. We show that the two methods as well as their results are equivalent.
Key words: Higher order dispersive nonlinear Schrödinger equation, The -expansion method, the exp -expansion method, exact solutions.