Pure-cubic optical solitons by Jacobi's elliptic function approach

In this paper, we focus on the investigation of optical solitons for ultrashort pulses modeled by the generalized nonlinear Schrödinger equation (NLSE) of third order. The governing model is dealt with by means of auxiliary equation method. The traveling wave theory is applied to reduce the governing model to the elliptic-like equation. Implementing the proposed mathematical tool leads to abundant Jacobi elliptic function (JEFs) solutions which degenerate to hyperbolic function solutions as the modulus of JEFs approaches 1. Accordingly, different forms of optical wave structures including dark, bright, singular, dark-singular and combined singular solitons are derived with existence conditions. The evolutions of some obtained results are displayed graphically which may provide the physical meaning of the complex phenomena related to the governing model.