Chaotic behavior and solitary wave solutions of stochastic-fractional Drinfel’d–Sokolov–Wilson equations with Brownian motion

The stochastic-fractional Drinfel’d-Sokolov-Wilson equation is a precently improved nonlinear partial differential equation in electromagnetism and fluid mechanics. Using the theory of planar dynamical systems, the authors first analyzed chaotic behavior, including sensitivity, Poincaré section and Lyapunov exponent, and then constructed solitary waves and periodic solutions. Secondly, the author analyzed the effects of random noise and fractional derivatives on the solution. Finally, a comparative study was conducted to demonstrate the innovation of this study. The methods and results of this paper can be applied to the study of a wider range of nonlinear wave phenomena.