A variety of new rogue wave patterns for three coupled nonlinear Maccari’s models in complex form

Maccari’s system serves as a valuable tool in various mathematical disciplines, contributing to the understanding of complex dynamics, control theory, synchronization phenomena, and mathematical modeling. This study utilizes the truncated Painlevé approach (TPA) to investigate the three coupled nonlinear Maccari’s equations in complex form. By using this technique, the localized solutions have been found and expressed in terms of arbitrary functions. These solutions included multirogue waves, rogue wave doublets, and lump solutions. The dynamical behavior of these solutions is visualized by selecting arbitrary values for the control parameters. Moreover, the studied model undergoes analysis from multiple perspectives, including quasi-periodic, chaotic motion, and multistability. An external periodic perturbation is introduced to the system, allowing the utilization of various chaos detecting tools. Through these tools, we identify quasi-periodic and chaotic behavior, demonstrating the system’s deviation from regular patterns. It is worth noting that all calculations were verified using Maple for accuracy and reliability. The analysis in the given research will enhance our comprehension of the behavior of waves in high-dimensional Maccari systems.