Dynamical analysis and optical soliton wave profiles to GRIN multimode optical fiber under the effect of noise

In this paper, the stochastic 2-dimensional nonlinear Schrödinger equation with multiplicative Brownian motion is investigated. This equation deals with beam propagation in a Graded-Index multimode optical fiber with a parabolic index profile. The spectral, temporal, and spatial features of ultrashort light pulses can be controlled in novel ways by this kind of nonlinear multimode optical fiber, which is gaining popularity. The bifurcation analysis, chaotic and sensitivity behavior of the wave solutions are examined using the qualitative theory for planar dynamical systems. The generalized exponential rational functional method is used to get the exact optical soliton solutions under the effect of noise. This method provides us the rational, exponential, dark, bright, combined dark-bright, singular, and solitary waveform solutions. Moreover, we use the MATHEMATICA11.1 tools to plot the 3-dimensional, 2-dimensional, and their corresponding contour diagrams to show the effects of multiplicative time noise on the optical solitons for the GRIN multimode optical fiber. Finally, we will show the multiplicative Brownian motion stabilizes the solutions of 2D-nonlinear Schrödinger equation of Graded-Index multimode optical fiber a round zero.