Analysis of the stochastic perturbed Schrödinger–Hirota equation with Kerr law in the presence of spatio-temporal dispersion with bifurcation and chaotic phenomena along with soliton solutions

Abstract

The goal of this work is to use the complete discriminant system (CDS) of the polynomial method (CDSPM) to provide soliton solutions for the perturbed Schrödinger–Hirota equation (PSHE) with the Kerr law by taking the stochastic into consideration. We examine exact and analytical solutions, such as those for the hyperbolic function, trigonometric function, Jacobian elliptic function (JEF), and other solitary wave (SW) solutions. Moreover, we also analyze the qualitative analysis of the governing model by using the terms of chaos and bifurcation. The trajectories of chaotic behavior show exponential divergence, which indicates that small changes in the initial circumstances cause the trajectories to become widely separated and divergent over time. We also discuss the phase portraits, which are useful in figuring out if the system’s equilibrium points are stable. Finally, we examine our governing model’s sensitivity analysis under different initial conditions. Sensitivity analysis measures a system’s or model’s robustness or sensitivity to changes in its input variables. Furthermore, we have included a number of graphs that clearly show the impact of the white noise so that you can better comprehend our results. The white noise effect is a distinct pattern of random fluctuations that may be seen in a variety of systems and incidents. It is distinguished by a uniform distribution of frequencies throughout the spectrum, resulting in a continuous and uncorrelated signal.