Abundant optical soliton solutions for the stochastic fractional fokas system using bifurcation analysis

Abstract

In this study, the stochastic fractional Fokas system (SFFS) with M-truncated derivatives is considered. A certain wave transformation is applied to convert this system to a one-dimensional conservative Hamiltonian system. Based on the qualitative theory of dynamical systems, the bifurcation and phase portrait are examined. Utilizing the conserved quantity, we construct some new traveling wave solutions for the SFFS. Due to the fact that the Fokas system is used to explain nonlinear pulse transmission in mono-mode optical fibers, the given solutions may be applied to analyze an extensive variety of crucial physical phenomena. To clarify the effects of the M-truncated derivative and Wiener process, the dynamic behaviors of the various obtained solutions are depicted with 3-D and 2-D curves.

Exploring the Exact Solution of the Space-Fractional Stochastic Regularized Long Wave Equation: A Bifurcation Approach

“…Using both fractional and stochastic generalizations in one model offers a more flexible tool for modeling systems that exhibit both memory effects and randomness. Research on stochastic fractional differential equations (SFDEs) is a growing area in applied mathematics, e.g., [20][21][22][23][24][25][26][27].…”