Exact solutions of the stochastic fractional long–short wave interaction system with multiplicative noise in generalized elastic medium

Abstract

The long–short wave interaction system (L-SWIS) is an important model describing the interaction of two waves propagating in a generalized elastic medium. In this study, the bifurcation and the influence of random interaction on the exact solution of the stochastic fractional long–short wave interaction system (SFL-SWIS) with multiplicative Brownian motion are studied, where the derivative refers to the modified Riemann–Liouville definition. After the Hamiltonian system is established by traveling wave transformation and first-order integration, we obtain abundant exact parametric solutions of SFL-SWIS. Also, the three-dimensional graph of some obtained results are drawn by using the symbolic calculation software Maple, which is used to show the influence of fractional derivative and random interaction on the solution. The obtained solitary wave solutions and exact solutions include the elliptic function solution, trigonometric function solution, exponential function solution and singular periodic solution. This study is the first to investigate the bifurcation and exact solution of SFL-SWIS, and the obtained results are theoretically and practically important to the propagation of optical signals, plasma waves and ocean waves.