Chaotic perturbations of solitons in complex conformable Maccari system

M. Mossa Al-Sawalha; Safyan Mukhtar; Azzh Saad Alshehry; Mohammad Alqudah; Musaad S. Aldhabani; M. Mossa Al-Sawalha; Safyan Mukhtar; Azzh Saad Alshehry; Mohammad Alqudah; Musaad S. Aldhabani

doi:10.3934/math.2025305

AIMS Mathematics

2025, Volume 10, Issue 3: 6664-6693. doi: 10.3934/math.2025305

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Chaotic perturbations of solitons in complex conformable Maccari system

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Basic Sciences, General Administration of Preparatory Year, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia
3.
Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia
4.
Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
5.
Department of Basic Sciences, School of Electrical Engineering & Information Technology, German Jordanian University, Amman 11180, Jordan
6.
Department of Mathematics, Faculty of Science, University of Tabuk, P.O.Box741, Tabuk 71491, Saudi Arabia

Received: 25 December 2024 Revised: 21 February 2025 Accepted: 28 February 2025 Published: 25 March 2025
MSC : 34G20, 35A20, 35A22, 35R11

In this research work, we use the generalized Bernoulli equation method (gBEM) to investigate the chaotic nature of solitons in complex structured conformable coupled Maccari system (CCMS) which is a fractional generalization of a nonlinear model coupled Maccari system (CMS) initially created to simulate hydraulic systems. This key model has numerous applications in several disciplines such as hydrodynamics, optics, quantum mechanics and plasma physics. The proposed gBEM converts the CCMS into a set of nonlinear ordinary differential equations (NODEs) to construct fresh plethora of soliton solutions in the form of rational, trigonometric, hyperbolic, and exponential functions. To comprehend the dynamics of acquired solitons in CCMS, a series of 3D and counter plots are used which graphically illustrate and reveal two types of chaotic perturbations, namely axial and periodic perturbations in the acquired solitons. Furthermore, the efficiency and adaptability of our method in handling a range of nonlinear models in mathematical science and engineering are confirmed by our computational work.
Citation: M. Mossa Al-Sawalha, Safyan Mukhtar, Azzh Saad Alshehry, Mohammad Alqudah, Musaad S. Aldhabani. Chaotic perturbations of solitons in complex conformable Maccari system[J]. AIMS Mathematics, 2025, 10(3): 6664-6693. doi: 10.3934/math.2025305

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Abstract

In this research work, we use the generalized Bernoulli equation method (gBEM) to investigate the chaotic nature of solitons in complex structured conformable coupled Maccari system (CCMS) which is a fractional generalization of a nonlinear model coupled Maccari system (CMS) initially created to simulate hydraulic systems. This key model has numerous applications in several disciplines such as hydrodynamics, optics, quantum mechanics and plasma physics. The proposed gBEM converts the CCMS into a set of nonlinear ordinary differential equations (NODEs) to construct fresh plethora of soliton solutions in the form of rational, trigonometric, hyperbolic, and exponential functions. To comprehend the dynamics of acquired solitons in CCMS, a series of 3D and counter plots are used which graphically illustrate and reveal two types of chaotic perturbations, namely axial and periodic perturbations in the acquired solitons. Furthermore, the efficiency and adaptability of our method in handling a range of nonlinear models in mathematical science and engineering are confirmed by our computational work.

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