This article discusses the (2 + 1)-dimensional Hirota-Maccari (HM) model, a particular type of Schrödinger equation that addresses various nonlinear phenomena in physics, optics, fluid dynamics, plasma physics, and other scientific areas. It uses a variable relation to transform the system into an ordinary form and builds different soliton solutions using the \(\left( {\frac{{G^{\prime } }}{{G^{2} }}} \right)\) -expansion and generalized \(\left( {\frac{{G^{\prime } }}{G}} \right)\) -expansion approaches. We create double periodic waves, dark solitons, bright solitons, anti-compacton solitons, bright dark breather waves, periodic multiple waves, multiple dark-bright breather waves, compactons, and \(W\) -shaped periodic waves using the above methods plus a soft computing package. We numerically simulate some results in 3D with density, 2D, and contour formats. Additionally, we converted the dynamic planner structure of the governing model using the Galilean transformation. We then studied the chaotic properties of this model using various chaos-detecting tools, including fractal dimensions, basins of attraction, recurrence maps, strange attractors, multistability, and return maps. The significance of this study lies in its ability to bridge the theoretical understanding of the governing model with potential applications in diverse nonlinear physical systems. To our knowledge, these two methods have not yet yielded any solutions to the underlying model.
