Dynamic effects on traveling wave solutions of the space-fractional long-short-wave interaction system with multiplicative white noise

In this paper, the stochastic space-fractional long-short-wave interaction system (SF-LSWIS) with multiplicative white noise is considered. The stochastic exact solutions, including triangular function solutions, hyperbolic function solutions, and Jacobi elliptic function solutions, are obtained via the complete discriminant system for polynomial method. For this purpose, the traveling wave transformation is applied to carry out the ordinary differential equation of this model, which is also converted to a dynamical system. Thereafter, qualitative behavior and bifurcation of the phase portraits of the dynamical system are investigated using the qualitative theory of dynamical systems. The chaotic behaviors of the system considering external periodic perturbation are studied. Furthermore, the 3D surface, graphs of contour plots, and level curves of some exact solutions are depicted by choosing proper parameter values. The influence and effect of fractional derivatives and noise strength on the solutions are also studied.