Investigation of different wave structures to the generalized third-order nonlinear Scrödinger equation

The present paper explores the generalized third-order nonlinear Schrödinger (GTONLS) equation which is used to model ultra-short pulses in optical fibers. The analysis is carried out systematically by adopting a complex transformation for reducing the GTONLS equation to a couple of nonlinear ordinary differential equations (NLODEs) with specific conditions such that the resulting NLODEs can be solved through the use of well-designed techniques such as the expa -function and unified methods. As an outcome, different wave structures including dark and bright solitons as well as Jacobi elliptic solutions to the model are formally constructed.