Dynamical behaviors, chaotic pattern and multiple optical solitons for coupled stochastic Schrödinger–Hirota system in magneto-optic waveguides with multiplicative white noise via Itô calculus

The primary focus of this study was on exploring the optical soliton solutions and chaotic patterns in magneto-optic waveguides through the coupled stochastic Schrödinger–Hirota equation with multiplicative white noise. Firstly, by means of traveling wave transformations and homogeneous balance principle, the coupled stochastic Schrödinger–Hirota equation in magneto-optic waveguides is transformed into ordinary differential equation. By selecting some suitable parameters, phase diagrams are plotted with the help of the mathematical software Maple. Secondly, the optical soliton solutions of the coupled stochastic Schrödinger–Hirota equation corresponding to phase orbits can be easily deduced through the method of dynamical systems. In addition, chaotic behavior for the coupled stochastic Schrödinger–Hirota system with perturbation term has been discussed in detail. Finally, the two-dimensional and three-dimensional graphs of the stochastic Schrödinger–Hirota equation are drawn, which further explain the propagation of the coupled stochastic Schrödinger–Hirota equation in nonlinear optics.