Bifurication analysis, chaotic behaviors and optical solitons with cubic-quintic-septic-nonic nonlinearity

The nonlinear Schrödinger equation (NLSE) is a fundamental model in physics relevant to fields such as nonlinear optics, Bose–Einstein condensates, and fiber optics. This study explores the fascinating realm of optical solitons, bifurcation analysis, and chaotic behaviors that result from the NLSE with cubic-quintic-septic-nonic nonlinearity of self-phase modulation. First, we transform the governing model into a system of ordinary differential equations by applying Lie symmetry analysis. Subsequently, we employ direct integration and the extended tanh method to reveal certain invariant and optical soliton solutions. Furthermore, we convert the system into a planar dynamical system using a specific transformation, which allows us to perform a comprehensive bifurcation analysis. By examining the various bifurcation scenarios, we understand the system’s behavior under different conditions and parameter values. Additionally, we introduce certain external perturbation terms into the system and observe the emergence of chaotic behavior.