Novel stochastic multi breather type, a-periodic, hybrid periodic and other type of waves of the Shrödinger-Hirota model with Wiener process

Abstract The current manuscript elaborate a novel characteristic of stochastic multi breather type, periodic, hybrid periodic and different type of waves solutions for the Shrödinger-Hirota (SH) equation. The mentioned equation is studied by a Wiener process and white noise which is used for the sudden and large-scale fluctuation. By applying the wave transformation technique the considered equation is transformed into ordinary differential equations, gives meaningful analysis. From the solution of the SH equation various type of results, including soliton, dark, bright, hybrid and periodic solitons. To visually capture these intricate behaviors, we employ MATLAB tools to generate 2D and 3D graphs of the analytical stochastic solutions. This combination of mathematical rigor and numerical simulations provides a comprehensive understanding of the phenomena under study, making a valuable contribution to the field of nonlinear wave equations and stochastic processes.