A study of dynamical features and novel soliton structures of complex-coupled Maccari's system

Naseem Abbas; Amjad Hussain; Mohsen Bakouri; Thoraya N. Alharthi; Ilyas Khan; Naseem Abbas; Amjad Hussain; Mohsen Bakouri; Thoraya N. Alharthi; Ilyas Khan

doi:10.3934/math.2025141

AIMS Mathematics

2025, Volume 10, Issue 2: 3025-3040. doi: 10.3934/math.2025141

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Research article

A study of dynamical features and novel soliton structures of complex-coupled Maccari's system

1.
Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000, Pakistan
2.
Department of Medical Equipment Technology, College of Applied Medical Science, Majmaah University, Majmaah 11952, Saudi Arabia
3.
Department of Physics, College of Arts, Fezzan University, Traghen 71340, Libya
4.
Department of Mathematics, College of Science, University of Bisha, P.O. Box 551, Bisha 61922, Saudi Arabia
5.
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
6.
Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman, Jordan

Received: 27 December 2024 Revised: 22 January 2025 Accepted: 10 February 2025 Published: 18 February 2025
MSC : 35C08

This investigation focuses on solitary wave solutions and dynamic analysis of the complex coupled Maccari system. We employ the new extended hyperbolic function method to establish bright-wave and dark-wave profiles of the model. The resulting solutions include hyperbolic, trigonometric, and exponential-type functions. Furthermore, we explore the model's dynamical characteristics via multiple perspectives, including phase portrait analysis, quasi-periodic and chaotic patterns, sensitivity analysis and Lyapunov exponent. The analysis validates the robustness of the new extended hyperbolic function method on one hand and extends the understanding of complex wave structures in Maccari's system on the other hand.
- complex coupled Maccari system,
- nonlinear optics,
- soliton solutions,
- Chaos,
- bifurcation analysis and sensitivity
Citation: Naseem Abbas, Amjad Hussain, Mohsen Bakouri, Thoraya N. Alharthi, Ilyas Khan. A study of dynamical features and novel soliton structures of complex-coupled Maccari's system[J]. AIMS Mathematics, 2025, 10(2): 3025-3040. doi: 10.3934/math.2025141

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Abstract

This investigation focuses on solitary wave solutions and dynamic analysis of the complex coupled Maccari system. We employ the new extended hyperbolic function method to establish bright-wave and dark-wave profiles of the model. The resulting solutions include hyperbolic, trigonometric, and exponential-type functions. Furthermore, we explore the model's dynamical characteristics via multiple perspectives, including phase portrait analysis, quasi-periodic and chaotic patterns, sensitivity analysis and Lyapunov exponent. The analysis validates the robustness of the new extended hyperbolic function method on one hand and extends the understanding of complex wave structures in Maccari's system on the other hand.

References

[1]	S. Zhang, Exp-function method for solving Maccari's system, Phys. Lett. A, 371 (2007), 65–71. https://doi.org/10.1016/j.physleta.2007.05.091 doi: 10.1016/j.physleta.2007.05.091
[2]	S. Y. Arafat, K. Fatema, M. E. Islam, M. A. Akbar, Promulgation on various genres soliton of Maccari system in nonlinear optics, Opt. Quant. Electron., 54 (2022), 206. https://doi.org/10.1007/s11082-022-03576-0 doi: 10.1007/s11082-022-03576-0
[3]	A. Maccari, The Kadomtsev-Petviashvili equation as a source of integrable model equations, J. Math. Phys., 37 (1996), 6207–6212. https://doi.org/10.1063/1.531773 doi: 10.1063/1.531773
[4]	N. Cheemaa, S. Chen, A. R. Seadawy, Propagation of isolated waves of coupled nonlinear (2+1)-dimensional Maccari system in plasma physics, Results Phys., 17 (2020), 102987. https://doi.org/10.1016/j.rinp.2020.102987 doi: 10.1016/j.rinp.2020.102987
[5]	R. Ali, D. Kumar, A. Akgul, A. Altalbe, On the periodic soliton solutions for fractional Schrodinger equations, Fractals, 32 (2024), 2440033. https://doi.org/10.1142/S0218348X24400334 doi: 10.1142/S0218348X24400334
[6]	M. G. Hafez, M. N. Alam, M. A. Akbar, Traveling wave solutions for some important coupled nonlinear physical models via the coupled Higgs equation and the Maccari system, J. King Saud Uni. Sci., 27 (2015), 105–112. https://doi.org/10.1016/j.jksus.2014.09.001 doi: 10.1016/j.jksus.2014.09.001
[7]	M. G. Hafez, B. Zheng, M. A. Akbar, Exact travelling wave solutions of the coupled nonlinear evolution equation via the Maccari system using novel $(G^{'}/G)$-expansion method, Egypt. J. Basic Appl. Sci., 2 (2015), 206–220. https://doi.org/10.1016/j.ejbas.2015.04.002 doi: 10.1016/j.ejbas.2015.04.002
[8]	M. Inc, A. I. Aliyu, A. Yusuf, D. Baleanu, E. Nuray, Complexiton and solitary wave solutions of the coupled nonlinear Maccari's system using two integration schemes, Modern Phys. Lett. B, 32 (2018), 1850014. https://doi.org/10.1142/S0217984918500148 doi: 10.1142/S0217984918500148
[9]	H. Kumar, F. Chand, Exact traveling wave solutions of some nonlinear evolution equations, J. Theor. Appl. Phys., 8 (2014), 114. https://doi.org/10.1007/s40094-014-0114-z doi: 10.1007/s40094-014-0114-z
[10]	H. Bulut, G. Yel, H. M. Baskonus, Novel structure to the coupled nonlinear Maccari's system by using modified trial equation method, Adv. Math. Models Appl., 2 (2017), 14–19.
[11]	T. Xu, Y. Chen, Z. Qiao, Multi-dark soliton solutions for the (2+1)-dimensional multi-component Maccari system, Modern Phys. Lett. B, 33, (2019), 1950390. https://doi.org/10.1142/S0217984919503901 doi: 10.1142/S0217984919503901
[12]	A. Neirameh, New analytical solutions for the coupled nonlinear Maccari's system, Alex. Eng. J., 55 (2016), 2839–2847. https://doi.org/10.1016/j.aej.2016.07.007 doi: 10.1016/j.aej.2016.07.007
[13]	N. Cheemaa, M. Younis, New and more exact traveling wave solutions to integrable (2+1)-dimensional Maccari system, Nonlinear Dyn., 83 (2016), 1395–1401. https://doi.org/10.1007/s11071-015-2411-8 doi: 10.1007/s11071-015-2411-8
[14]	A. Saha, S. Banerjee, Dynamical systems and nonlinear waves in plasmas, New York: CRC Press, 2021. https://doi.org/10.1201/9781003042549
[15]	N. K. Pal, P. Chatterjee, A. Saha, Solitons, multi-solitons and multi-periodic solutions of the generalized Lax equation by Darboux transformation and its quasiperiodic motions, Int. J. Modern Phys. B, 38 (2023), 2440001. https://doi.org/10.1142/S0217979224400010 doi: 10.1142/S0217979224400010
[16]	A. Jhangeer, W. A. Faridi, M. Alshehri, Soliton wave profiles and dynamical analysis of fractional Ivancevic option pricing model, Sci. Rep., 14 (2024), 23804. https://doi.org/10.1038/s41598-024-74770-1 doi: 10.1038/s41598-024-74770-1
[17]	N. Abbas, A. Hussain, Novel soliton structures and dynamical behaviour of coupled Higgs field equations, Eur. Phys. J. Plus, 139 (2024), 327. https://doi.org/10.1140/epjp/s13360-024-05124-z doi: 10.1140/epjp/s13360-024-05124-z
[18]	A. Hussain, N. Abbas, S. Niazai, I. Khan, Dynamical behavior of Lakshamanan-Porsezian-Daniel model with spatiotemporal dispersion effects, Alex. Eng. J., 96, (2024), 332–343. https://doi.org/10.1016/j.aej.2024.03.024 doi: 10.1016/j.aej.2024.03.024
[19]	A. Hussain, N. Abbas, Periodic, quasi-periodic, chaotic waves and solitonic structures of coupled Benjamin-Bona-Mahony-KdV system, Phys. Scr., 99 (2024), 125231. https://doi.org/10.1088/1402-4896/ad896b doi: 10.1088/1402-4896/ad896b
[20]	V. I. Arnold, Ordinary differential equations, Berlin: Springer Science & Business Media, 1992.
[21]	R. Ali, E. Tag-eldin, A comparative analysis of generalized and extended $(G^\prime/G)$-Expansion methods for traveling wave solutions of fractional Maccari's system with complex structure, Alex. Eng. J., 79, (2023) 508–530. https://doi.org/10.1016/j.aej.2023.08.007 doi: 10.1016/j.aej.2023.08.007
[22]	Z. M. Emad, S. S. M. A. Shehata, M. N. Alam, A. Lanre, Exact propagation of the isolated waves model described by the three coupled nonlinear Maccari's system with complex structure, Int. J. Modern Phys. B, 35 (2021), 2150193. https://doi.org/10.1142/S0217979221501939 doi: 10.1142/S0217979221501939
[23]	H. U. Rehman, M. A. Imran, N. Ullah, A. Akgul, Exact solutions of (2+1)‐dimensional Schrodinger's hyperbolic equation using different techniques, Numer. Meth. PDE, 39 (2023), 4575–4594. https://doi.org/10.1002/num.22644 doi: 10.1002/num.22644
[24]	D. Jordan, P. Smith, Nonlinear ordinary differential equations: an introduction for scientists and engineers, Cambridge: OUP Oxford, 2007.

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