Bifurcation and traveling wave solutions of stochastic Manakov model with multiplicative white noise in birefringent fibers

Abstract

Manakov model is an extended form of Schrödinger equation. It is a coupled partial differential equation governing the dual-mode transmission of optical fiber communication and the deep-sea transportation with double-layer constraints. In this paper, the bifurcation and traveling wave solutions of the stochastic Manakov model(SMM) describing the multiplicative white noise of optical signal propagation in birefringent fibers are studied. The research work is carried out in the following three steps. Firstly, by the help of traveling wave transformation and first integral, the SMM with multiplicative white noise is simplified to a 2D planar dynamic system. Secondly, the phase diagrams of the planar dynamic system are drawn to determine the possible traveling wave solutions. Finally, based on the classification of parameter group, combined with the elliptic integral technique, the solitary wave solutions and traveling wave solutions of SMM are constructed. The obtained bifurcation results reveal the dynamic behavior of SMM from a geometric point of view. According to the phase portraits, we get abundant solitary wave solutions and traveling wave solutions, including elliptic function periodic solution, trigonometric function solution and singular periodic solution. This is the first study on the bifurcation of SMM with multiplicative white noise, and the obtained results provide the propagation of optical solitons in nonlinear optics.