Qualitative analysis of stochastic Schrödinger–Hirota equation in birefringent fibers with spatiotemporal dispersion and parabolic law nonlinearity

Abstract

In this paper, the stochastic Schrödinger–Hirota equation in birefringent fibers with spatiotemporal dispersion and parabolic law nonlinearity is studied, which is usually used to describe the mathematical model of optical soliton propagation in dispersive optical fibers from the field of nonlinear optics. Firstly, the stochastic Schrödinger–Hirota equation is converted into two-dimensional planar dynamic system by using the traveling wave transformation. Secondly, the qualitative analysis of the stochastic Schrödinger–Hirota equation is discussed by using the theory of planar dynamical systems. Finally, the chaos pattern of the stochastic Schrödinger–Hirota equation with perturbed system is considered. What is more, phase portraits and sensitivity analysis of the perturbed system are plotted by using the Maple software.