Comparative study of novel solitary wave solutions with unveiling bifurcation and chaotic structure modelled by stochastic dynamical system

Abstract In this study, we conduct a comprehensive investigation of the novel characteristics of the (2 + 1)-dimensional stochastic Hirota–Maccari System (SHMS), which is a prominent mathematical model with significant applications in the field of nonlinear science and applied mathematics. Specifically, SHMS plays a critical role in the study of soliton dynamics, nonlinear wave propagation, and stochastic effects in complex physical systems such as fluid dynamics, optics, and plasma physics. In order to account for the abrupt and significant fluctuation, the aforementioned system is investigated using a Wiener process with multiplicative noise in the Itô sense. The considered equation is studied by the new extended direct algebraic method (NEDAM) and the modified Sardar sub-equation (MSSE) method. By solving this equation, we systematically derived the novel soliton solutions in the form of dark, dark-bright, bright-dark, singular, periodic, exponential, and rational forms. Additionally, we also categorize and analyze the W -shape, M -shape, bell shape, exponential, and hyperbolic soliton wave solutions, which are not documented by researchers. The bifurcation, chaos and sensitivity analysis has been depicted which represent the applicability of the system in different dynamics. These findings greatly advance our knowledge of nonlinear wave events in higher-dimensional stochastic systems both theoretically and in terms of possible applications. These findings are poised to open new avenues for future research into the applicability of stochastic nonlinear models in various scientific and industrial domains.