The analysis of solitonic, supernonlinear, periodic, quasiperiodic, bifurcation and chaotic patterns of perturbed Gerdjikov–Ivanov model with full nonlinearity

Abstract

In this manuscript, the perturbed Gerdjikov–Ivanov equation is considered for the investigating model. It is studied to govern the dynamics of soliton propagation through optical fibers, metamaterials or PCF. The observed model is subjected to an extended simple equation technique, which disclosed an abundant of exact solutions including trigonometric function, singular, kink, peakon and compacton solutions. These solutions are made available with their essential conditions, which guarantee the persistence of such optical solitons and portraits using appropriate physical parameters in 3D, 2D and density plots. After that, the traveling wave transformation is used to turn the mth-order nonlinear perturbed Gerdjikov–Ivanov equation into a planar dynamical system. The dynamical and chaotic behaviors of the considered equation are also discussed. The qualitative analysis of the dynamical system and the chaotic behaviors of the perturbed system are investigated using the theory of plane dynamic systems. In addition, we utilize the RK4 method to discover patterns in the dynamical system that seem to be super nonlinear, periodic, and quasiperiodic. The reported results are new and have not been investigated. They can be used in the explanation of the physical phenomena modeled and will give information about the long-term dynamic behavior. Numerical simulations reveal that by changing the frequency and amplitude parameters have an impact on the dynamic behaviors of the system. It is established that the extended simple equation method and dynamical observations offer further influential mathematical tools for constructing exact solutions and their qualitative analysis in NLEEs in mathematical physics.