Dynamical properties and new optical soliton solutions of a generalized nonlinear Schrödinger equation

For exploring the behavior of complex two-dimensional systems, the idea of planar dynamical systems offers a potent and adaptable framework. It is simple for researchers to understand the dynamics of the system and acquire deeper insights into its behavior by visualizing trajectories in the ( x , y ) plane. Keeping this in mind, the complex dynamics of the nonlinear Schrödinger equation has not been explored using planar dynamical theory, in the literature. In this manuscript, the dynamical features and some new optical solitons are discussed for the considered NLSE. Using RK4 numerical technique, the dynamical features such as bifurcation, phase portraits, time series and sensitivity analysis are portrayed. Moreover, utilizing the traveling wave transformations and complete discriminant system method, some new optical solitary waves solutions are obtained which depends on trigonometric functions and Jacobi elliptic functions. These solutions are new and have not been reported in the literature for the considered equation.