Wave Dynamics in Design: The Role of Nonlinear Potential Burgers' Equation With Variable Coefficients.

This paper investigates exact solutions of the potential Burgers equation with variable coefficients (PBEVCs), contributing to communication engineering, nonlinear acoustics, and fluid mechanics. It explores novel solutions using the improved modified extended tanh–function method (IMETFM), revealing diverse characteristics and providing deeper insights into nonlinear wave dynamics. The study also analyzes the long‐term behavior of PBEVC under noise influence, highlighting insights into noise‐perturbed systems' robustness. Moreover, it establishes connections to practical applications like 5G optical fiber transmission and ocean wave oscillations, showcasing the wide applicability of the IMETFM approach. This work's novelty lies in uncovering diverse solution characteristics and bridging theoretical understanding with real‐world applications. [ABSTRACT FROM AUTHOR]