Unveiling New Perspectives on the Hirota–Maccari System With Multiplicative White Noise

ABSTRACT In this study, we delve into the stochastic Hirota–Maccari system, which is subjected to multiplicative noise according to the Itô sense. The stochastic Hirota–Maccari system is significant for its ability to accurately model how stochastic affects nonlinear wave propagation, providing valuable insights into complex systems like fluid dynamics and optical fibers. It enhances understanding of the interplay between noise and nonlinearity, benefiting both theoretical research and practical applications in stochastic nonlinear dynamics. Our primary objective is to uncover new insights into this system by utilizing the generalized Jacobi elliptic function method. Through this methodology, we reveal a spectrum of novel solutions, including Jacobi elliptic functions, dark solitons, singular solitons, periodic waves, and Weierstrass elliptic functions. Numerical results illustrate the behavior of these solutions under different noise strengths, confirming their robustness. Furthermore, a comparative analysis with existing methodologies highlights the advantages of our approach in capturing stochastic effects in nonlinear wave dynamics. Comprehensive numerical tables and visualizations, including 3D, 2D, and contour plots, provide deeper insight into the system's dynamics, reinforcing its applicability to fields such as material science and biophysics.