The novel stochastic structure of solitary waves to the stochastic Maccari's system via Wiener process

M. B. Almatrafi; Mahmoud A. E. Abdelrahman; M. B. Almatrafi; Mahmoud A. E. Abdelrahman

doi:10.3934/math.2025056

AIMS Mathematics

2025, Volume 10, Issue 1: 1183-1200. doi: 10.3934/math.2025056

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The novel stochastic structure of solitary waves to the stochastic Maccari's system via Wiener process

M. B. Almatrafi ¹,
Mahmoud A. E. Abdelrahman ^{1,2
,
,}

1.
Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt

Received: 27 October 2024 Revised: 11 December 2024 Accepted: 18 December 2024 Published: 20 January 2025
MSC : 34A34, 35C07, 35Q62

This article investigates the nonlinear Maccari model with multiplicative noise using the unified technique. Numerous new important solitary wave solutions are presented with free physical parameters. These solutions play a vital role in various domains, including nonlinear optics, plasma physics, and hydrodynamics. The investigation shows that the solution process is quick and clear, where a comparatively higher number of novel solutions are obtained. The performance of the used approach is compared with that of other methods. We create 2D and 3D graphs for certain solutions of the study, utilizing suitably selected values for the physical parameters. We also address the impact of model parameters on the solution characteristics. We observe that our results may help to resolve some physical problems in the actual world by determining the motion of a single wave in a tiny region. Finally, the outcomes show how simple and effective this method is at producing rich, accurate solutions to nonlinear models in mathematical physics as well as complex nonlinear wave structures.
- Maccari system,
- unified method,
- Wiener process,
- solitary wave solution,
- nonlinearity structures
Citation: M. B. Almatrafi, Mahmoud A. E. Abdelrahman. The novel stochastic structure of solitary waves to the stochastic Maccari's system via Wiener process[J]. AIMS Mathematics, 2025, 10(1): 1183-1200. doi: 10.3934/math.2025056

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Abstract

This article investigates the nonlinear Maccari model with multiplicative noise using the unified technique. Numerous new important solitary wave solutions are presented with free physical parameters. These solutions play a vital role in various domains, including nonlinear optics, plasma physics, and hydrodynamics. The investigation shows that the solution process is quick and clear, where a comparatively higher number of novel solutions are obtained. The performance of the used approach is compared with that of other methods. We create 2D and 3D graphs for certain solutions of the study, utilizing suitably selected values for the physical parameters. We also address the impact of model parameters on the solution characteristics. We observe that our results may help to resolve some physical problems in the actual world by determining the motion of a single wave in a tiny region. Finally, the outcomes show how simple and effective this method is at producing rich, accurate solutions to nonlinear models in mathematical physics as well as complex nonlinear wave structures.

References

[1]	A. R. Alharbi, M. B. Almatrafi, Exact solitary wave and numerical solutions for geophysical KdV equation, J. King Saud Univ. Sci., 34 (2022), 102087. https://doi.org/10.1016/j.jksus.2022.102087 doi: 10.1016/j.jksus.2022.102087
[2]	M. B. Almatrafi, Abundant traveling wave and numerical solutions for Novikov-Veselov system with their stability and accuracy, Appl. Anal., 102 (2023), 2389–2402. https://doi.org/10.1080/00036811.2022.2027381 doi: 10.1080/00036811.2022.2027381
[3]	X. M. Wang, S. A. Javed, A. Majeed, M. Kamran, M. Abbas, Investigation of exact solutions of nonlinear evolution equations using unified method, Mathematics, 10 (2022), 1–17. https://doi.org/10.3390/math10162996 doi: 10.3390/math10162996
[4]	R. Ali, S. Barak, A. Altalbe, Analytical study of soliton dynamics in the realm of fractional extended shallow water wave equations, Phys. Scr., 99 (2024), 065235. https://doi.org/10.1088/1402-4896/ad4784 doi: 10.1088/1402-4896/ad4784
[5]	N. Sajid, Z. Perveen, M. Sadaf, G. Akram, M. Abbas, T. Abdeljawad, et al., Implementation of the Exp-function approach for the solution of KdV equation with dual power law nonlinearity, Comput. Appl. Math., 41 (2022), 338. https://doi.org/10.1007/s40314-022-02047-2 doi: 10.1007/s40314-022-02047-2
[6]	M. B. Almatrafi, A. Alharbi, New soliton wave solutions to a nonlinear equation arising in plasma physics, Comput. Model. Eng. Sci., 137 (2023), 827–841. https://doi.org/10.32604/cmes.2023.027344 doi: 10.32604/cmes.2023.027344
[7]	M. A. E. Abdelrahman, G. Alshreef, Closed-form solutions to the new coupled Konno-Oono equation and the Kaup-Newell model equation in magnetic field with novel statistic application, Eur. Phys. J. Plus, 136 (2021), 455. https://doi.org/10.1140/epjp/s13360-021-01472-2 doi: 10.1140/epjp/s13360-021-01472-2
[8]	H. G. Abdelwahed, E. K. El-Shewy, R. Sabry, M. A. E. Abdelrahman, Characteristics of stochastic Langmuir wave structures in presence of Itô sense, Results Phys., 37 (2022), 105435. https://doi.org/10.1016/j.rinp.2022.105435 doi: 10.1016/j.rinp.2022.105435
[9]	R. A. Alomair, S. Z. Hassan, M. A. E. Abdelrahman, A. H. Amin, E. K. El-Shewy, New solitary optical solutions for the NLSE with $\delta$-potential through Brownian process, Results Phys., 40 (2022), 105814. https://doi.org/10.1016/j.rinp.2022.105814 doi: 10.1016/j.rinp.2022.105814
[10]	H. Yasmin, A. S. Alshehry, A. H. Ganie, A. Shafee, R. Shah, Noise effect on soliton phenomena in fractional stochastic Kraenkel-Manna-Merle system arising in ferromagnetic materials, Sci. Rep., 14 (2024), 1810. https://doi.org/10.1038/s41598-024-52211-3 doi: 10.1038/s41598-024-52211-3
[11]	I. Karatzas, S. E. Shreve, Brownian motion and stochastic calculus, New York: Springer, 1998. https://doi.org/10.1007/978-1-4612-0949-2
[12]	H. Pishro-Nik, Introduction to probability, statistics, and random processes, Kappa Research, 2014.
[13]	M. A. E. Abdelrahman, E. K. El-Shewy, Y. Omar, N. F. Abdo, Modulations of collapsing stochastic modified NLSE structures, Mathematics, 11 (2023), 1–12. https://doi.org/10.3390/math11204330 doi: 10.3390/math11204330
[14]	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
[15]	G. H. Wang, L. H. Wang, J. G. Rao, J. S. He, New patterns of the two-dimensional rogue waves: (2+1)-dimensional Maccari system, Commun. Theor. Phys., 67 (2017), 601. http://iopscience.iop.org/0253-6102/67/6/601
[16]	T. Xu, Y. Chen, Z. J. 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
[17]	R. A. Alomair, S. Z. Hassan, M. A. E. Abdelrahman, A new structure of solutions to the coupled nonlinear Maccari's systems in plasma physics, AIMS Math., 7 (2022), 8588–8606. https://doi.org/10.3934/math.2022479 doi: 10.3934/math.2022479
[18]	A. Maccari, The Maccari system as model system for rogue waves, Phys. Lett. A, 384 (2020), 126740. https://doi.org/10.1016/j.physleta.2020.126740 doi: 10.1016/j.physleta.2020.126740
[19]	C. Moser, J. LaBelle, I. H. Cairns, High bandwidth measurements of auroral Langmuir waves with multiple antennas, Ann. Geophys., 40 (2022), 231–245. https://doi.org/10.5194/angeo-40-231-2022 doi: 10.5194/angeo-40-231-2022
[20]	C. Briand, P. Henri, V. Génot, N. Lormant, N. Dufourg, B. Cecconi, et al., STEREO database of interplanetary Langmuir electric waveforms, J. Geophys. Res. Space Phys., 121 (2016), 1062–1070. https://doi.org/10.1002/2015JA022036 doi: 10.1002/2015JA022036
[21]	S. T. Demiray, Y. Pandir, H. Bulut, New solitary wave solutions of Maccari system, Ocean Eng., 103 (2015), 153–159. https://doi.org/10.1016/j.oceaneng.2015.04.037 doi: 10.1016/j.oceaneng.2015.04.037
[22]	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
[23]	H. Zhao, Applications of the generalized algebraic method to special-type nonlinear equations, Chaos Solitons Fract., 36 (2008), 359–369. https://doi.org/10.1016/j.chaos.2006.06.060 doi: 10.1016/j.chaos.2006.06.060
[24]	H. G. Abdelwahed, A. F. Alsarhana, E. K. El-Shewy, M. A. E. Abdelrahman, The stochastic structural modulations in collapsing Maccari's model solitons, Fractal Fract., 7 (2023), 1–12. https://doi.org/10.3390/fractalfract7040290 doi: 10.3390/fractalfract7040290
[25]	H. Alhazmi, S. A. Bajri, E. K. El-Shewy, M. A. E. Abdelrahman, Effect of random noise behavior on the properties of forcing nonlinear Maccari's model structures, AIP Adv., 14 (2024), 105330. https://doi.org/10.1063/5.0228465 doi: 10.1063/5.0228465
[26]	S. Zhao, Z. Li, The analysis of traveling wave solutions and dynamical behavior for the stochastic coupled Maccari's system via Brownian motion, Ain Shams Eng. J., 15 (2024), 103037. https://doi.org/10.1016/j.asej.2024.103037 doi: 10.1016/j.asej.2024.103037
[27]	S. Akcagil, T. Aydemir, A new application of the unified method, New Trends Math. Sci., 6 (2018), 185–199. http://dx.doi.org/10.20852/ntmsci.2018.261 doi: 10.20852/ntmsci.2018.261
[28]	T. S. Gill, C. Bedi, A. S. Bains, Envelope excitations of ion acoustic solitary waves in a plasma with superthermal electrons and positrons, Phys. Scr., 81 (2010), 055503. https://doi.org/10.1088/0031-8949/81/05/055503 doi: 10.1088/0031-8949/81/05/055503
[29]	M. J. Uddin, M. S. Alam, A. A. Mamun, Nonplanar positron-acoustic Gardner solitary waves in electron-positron-ion plasmas with superthermal electrons and positrons, Phys. Plasmas, 22 (2015), 022111. https://doi.org/10.1063/1.4907226 doi: 10.1063/1.4907226

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