Dynamics in (2+1)-dimensional complex coupled Maccari system: Bifurcation analysis, phase portraits and optical solitons

In this paper, we investigate the ([Formula: see text])-dimensional complex coupled Maccari system, which is an important component in understanding nonlinear wave interactions. We aim to find exact solutions that highlight the complex wave patterns. To achieve this, we apply the extended hyperbolic function method. The results demonstrate that various waveforms and patterns enhance our understanding of the system, revealing a wide variety of solutions of different types such as periodic, dark, singular-periodic, singular, bright optical solitons, and some rational functions. Additionally, we perform a bifurcation analysis to investigate the dynamic behavior and stability of these solutions. We identify parameter regions in which the system undergoes changes, which may enhance our capacity to predict and control the dynamics within the system. This model has several applications across a wide range of disciplines, including plasma physics, optical fibers, and fluid dynamics. To conduct extensive research and provide an improved depiction of the model, we present graphical representations in both 2D and 3D. Bifurcation analyses of the phase portraits of the ordinary differential equation related to the partial differential equation under study are also conducted. We highlight certain conditions that ensure the occurrence of the solutions we have found.