In this study, we investigate the \((2+1)\) -D Jaulent-Miodek (JM) equation, which is significant due to its energy-based Schrödinger potential and applications in fields such as optics, soliton theory, signal processing, geophysics, fluid dynamics, and plasma physics. Given its broad utility, a rigorous mathematical analysis of the JM equation is essential. The primary objective of this work is to derive exact soliton solutions using the Modified Sub-Equation (MSE) and Modified Auxiliary Equation (MAE) techniques. These solutions are computed using Maple 18, and encompass a variety of wave structures, including bright solitons, kink solitons, periodic waves, and singular solitons. The potential applications of these solutions span diverse domains, such as nonlinear dynamics, fiber optics, ocean engineering, software engineering, electrical engineering, and other areas of physical science. Through numerical simulations, we visualize the physical characteristics of the obtained soliton solutions using three distinct graphical formats: 3D surface plots, 2D contour plots, and line plots, based on the selection of specific parameter values. Our results demonstrate that the MSE and MAE techniques are not only efficient but also straightforward in extracting soliton solutions for the JM equation, outperforming other existing methods. Furthermore, the solutions presented in this study are novel, representing contributions that have not been previously reported in the literature.
