The fractional soliton solutions and dynamical investigation for planer Hamiltonian system of Fokas model in optical fiber
Muhammad Amin S. Murad, Waqas Ali Faridi, Adil Jhangeer, Mujahid Iqbal, Ahmed H. Arnous, Fairouz Tchier
Abstract
This research uses the Sardar sub-equation approach to study the optical soliton solutions of a time-fractional Fokas system that represents pulse propagation in mono-mode optical fiber . New optical solutions are derived in the mixed dark-bright, bright, wave, singular topological, and bell-shaped types by means of the current approach. The obtained solutions indicate that this method is very powerful for finding exact traveling wave solutions of nonlinear evolution equations. In order to visualize the propagation of developed soliton solutions, 2D, line plots, and 3D surface plots are depicted along with suitable parametric values. The first order dynamical system is constructed by using the Galilean transformation to develop the Hamiltonian function . The sensitivity analysis shows the dependability of the model under different initial conditions. The generated solutions guarantee that the approach used offers a strong and dynamic mathematical instrument to address a variety of non-linear wave issues. These optical solutions are ingenious and enthralling, with potential to advance our understanding of some diffusion processes and energy transfer in math models within different fields, i.e. pulse propagation in monomode optical fiber is considered.