Some new optical solitary waves solutions of a third order dispersive Schrödinger equation with Kerr nonlinearity using an efficient approach associated with Riccati equation

This manuscript delves into the exploration of a third-order dispersive Schrödinger equation incorporating Kerr nonlinear effects, a common model employed for the transmission of optical fiber pulses. Utilizing an effective analytical approach, the study unveils previously undiscovered exact solutions for the Schrödinger equation, with a primary focus on analyzing optical solitons within nonlinear Schrödinger equations. The proposed method leverages a Riccati equation, yielding solutions expressed in trigonometric and hyperbolic functions. Noteworthy are the captivating dynamics exhibited by the optical solitons across diverse spatial variables, denoted as x . All numerical results are executed using Mathematica software and are visually presented in both 2D and 3D space. Additionally, the manuscript elucidates the significance of these findings in advancing our understanding of optical soliton behavior within the realm of nonlinear Schrödinger equations.