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

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Abstract

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.

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through large group Research Project under grant number RGP2/347/44.

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The authors have not disclosed any funding.

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Author notes

  1. Nauman Raza and Nehad Ali Shah have contributed equally to this work and are co-first authors.

Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan

    Nauman Raza & Beenish Rani

  2. Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia

    Younes Chahlaoui

  3. Department of Mechanical Engineering, Sejong University, Seoul, 05006, South Korea

    Nehad Ali Shah

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  1. Nauman Raza
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  2. Beenish Rani
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  3. Younes Chahlaoui
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  4. Nehad Ali Shah
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Correspondence to Nauman Raza.

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Raza, N., Rani, B., Chahlaoui, Y. et al. A variety of new rogue wave patterns for three coupled nonlinear Maccari’s models in complex form. Nonlinear Dyn 111, 18419–18437 (2023). https://doi.org/10.1007/s11071-023-08839-3

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