Dynamical features and traveling wave structures of the perturbed Fokas-Lenells equation in nonlinear optical fibers

Abstract

In this study, the new complex wave solutions of the perturbed Fokas-Lenells (p-FL) equation, which has applications in nonlinear optical fibers are obtained using a new extended direct algebraic method. This model represents recent electronic communications like Internet blogs, facebook communication and twitter comments. The obtained solutions are the different classes of traveling wave structures with singular solutions Type-I \& II, dark-singular, dark, and dark-bright solutions. Furthermore, stability conditions for the computed structures are reported. Also, graphical representations of some particular structures are shown by taking the specific values of the constants. The ordinary differential equation (ODE) obtained from a traveling wave transformation is converted into a dynamical system using Galilean transformation. The phase plane analysis is done for different values of the controlled parameters $d_1$ and $d_3$. A perturbation term is added to analyze the chaotic dynamics, and plots indicate that the system shows the chaotic dynamics. Also, sensitivity analysis shows that the system is sensitive to initial conditions. The conclusion is accounted for toward the end.

Modeling Wave Packet Dynamics and Exploring Applications: A Comprehensive Guide to the Nonlinear Schrödinger Equation

“…Additionally, Muhammad et al delve into the complexities of the FL equation, utilizing an extended algebraic technique to find new wave solutions with nonlinear properties and analyze their propagation and stability. Notably, they introduce a disturbance to the equation and observe that the system exhibits chaotic dynamics and a strong dependence on initial conditions [57].…”

“…. , (57) with u n (x, X, t, τ 1 , τ 2 ), where X = ϵx, τ 1 = ϵt, and τ 2 = ϵ 2 t act as slower variables. Substituting (57) to the IVP ( 55) and ( 56) yields a series progressing in the order of ϵ.…”