Applications of soliton solutions of the two-dimensional nonlinear complex coupled Maccari equations

Mohammad Alqudah; Manoj Singh; Mohammad Alqudah; Manoj Singh

doi:10.3934/math.20241521

AIMS Mathematics

2024, Volume 9, Issue 11: 31636-31657. doi: 10.3934/math.20241521

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Applications of soliton solutions of the two-dimensional nonlinear complex coupled Maccari equations

Mohammad Alqudah ^{1
,},
Manoj Singh ^{2
,
,}

1.
Department of Basic Sciences, School of Electrical Engineering & Information Technology, German Jordanian University, Amman 11180, Jordan; Email: mohammad.qudah@gju.edu.jo
2.
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Kingdom of Saudi Arabia

Received: 19 September 2024 Revised: 16 October 2024 Accepted: 25 October 2024 Published: 07 November 2024
MSC : 34G20, 35A20, 35A22, 35R11

This study investigates the two-dimensional nonlinear complex coupled Maccari equations, which are significant in describing solitary waves concentrated in small spatial regions. These equations have applications across various fields, including hydrodynamics, nonlinear optics, and the study of sonic Langmuir solitons. Using the Bäcklund transformation, we explore a broad range of soliton solutions for this system, focusing on their spectral properties. The proposed method stands out for its simplicity and comprehensive results compared to traditional approaches. The obtained solutions are expressed in rigorous, trigonometric, and hyperbolic forms, providing deeper insights into the dynamics of the system. To enhance understanding, we present contour and three-dimensional graphical representations of the solutions. This study has potential applications in energy and industry by advancing the understanding of nonlinear wave phenomena, which are crucial in optimizing energy transfer processes and designing efficient systems in hydrodynamic and optical engineering. Additionally, the soliton solutions obtained here contribute to technologies in power transmission and high-speed optical communications, offering a foundation for innovations in sustainable energy systems and industrial applications.
Citation: Mohammad Alqudah, Manoj Singh. Applications of soliton solutions of the two-dimensional nonlinear complex coupled Maccari equations[J]. AIMS Mathematics, 2024, 9(11): 31636-31657. doi: 10.3934/math.20241521

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Abstract

This study investigates the two-dimensional nonlinear complex coupled Maccari equations, which are significant in describing solitary waves concentrated in small spatial regions. These equations have applications across various fields, including hydrodynamics, nonlinear optics, and the study of sonic Langmuir solitons. Using the Bäcklund transformation, we explore a broad range of soliton solutions for this system, focusing on their spectral properties. The proposed method stands out for its simplicity and comprehensive results compared to traditional approaches. The obtained solutions are expressed in rigorous, trigonometric, and hyperbolic forms, providing deeper insights into the dynamics of the system. To enhance understanding, we present contour and three-dimensional graphical representations of the solutions. This study has potential applications in energy and industry by advancing the understanding of nonlinear wave phenomena, which are crucial in optimizing energy transfer processes and designing efficient systems in hydrodynamic and optical engineering. Additionally, the soliton solutions obtained here contribute to technologies in power transmission and high-speed optical communications, offering a foundation for innovations in sustainable energy systems and industrial applications.

References

[1]	M. A. E. Abdelrahman, M. Kunik, The Ultra-Relativistic Euler equations, Math. Meth. Appl. Sci., 38 (2015), 247–1264. https://doi.org/10.1002/mma.3141 doi: 10.1002/mma.3141
[2]	M. A. E. Abdelrahman, Global solutions for the Ultra-Relativistic Euler equations, Nonlinear Anal., 155 (2017), 140–162. https://doi.org/10.1016/j.na.2017.01.014 doi: 10.1016/j.na.2017.01.014
[3]	M. A. E. Abdelrahman, On the shallow water equations, Z. Naturforsch., 72 (2017), 873–879. https://doi.org/10.1515/zna-2017-0146 doi: 10.1515/zna-2017-0146
[4]	P. Razborova, B. Ahmed, A. Biswas, Solitons, shock waves and conservation laws of Rosenau-KdV-RLW equation with power law nonlinearity, Appl. Math. Inf. Sci., 8 (2014), 485–491. https://doi.org/10.12785/amis/080205 doi: 10.12785/amis/080205
[5]	A. Biswas, M. Mirzazadeh, Dark optical solitons with power law nonlinearity using G' / G -expansion, Optik, 125 (2014), 4603–4608. https://doi.org/10.1016/j.ijleo.2014.05.035 doi: 10.1016/j.ijleo.2014.05.035
[6]	M. Singh, Fractional view analysis of coupled Whitham-Broer-Kaup and Jaulent-Miodek equations, Ain Shams Eng. J., 2024, 102830. https://doi.org/10.1016/j.asej.2024.102830 doi: 10.1016/j.asej.2024.102830
[7]	M. Singh, M. Tamsir, Y. S. El-Saman, S. Pundhir, Approximation of two-dimensional time-fractional Navier-Stokes equations involving Atangana-Baleanu derivative, Int. J. Math., Eng. Manag., 9 (2024). https://doi.org/10.33889/IJMEMS.2024.9.3.033 doi: 10.33889/IJMEMS.2024.9.3.033
[8]	S. Alshammari, M. M. Al-Sawalha, R. Shah, Approximate analytical methods for a fractional-order nonlinear system of Jaulent-Miodek equation with energy-dependent Schrodinger potential, Fractal Fract., 7 (2023), 140. https://doi.org/10.3390/fractalfract7020140 doi: 10.3390/fractalfract7020140
[9]	A. A. Alderremy, N. Iqbal, S. Aly, K. Nonlaopon, Fractional series solution construction for nonlinear fractional reaction-diffusion Brusselator model utilizing Laplace residual power series, Symmetry, 14 (2022), 1944. https://doi.org/10.3390/sym14091944 doi: 10.3390/sym14091944
[10]	M. M. Al-Sawalha, A. Khan, O. Y. Ababneh, T. Botmart, Fractional view analysis of Kersten-Krasil shchik coupled KdV-mKdV systems with non-singular kernel derivatives, AIMS Math., 7 (2022), 18334–18359. https://doi.org/10.3934/math.20221010 doi: 10.3934/math.20221010
[11]	E. M. Elsayed, K. Nonlaopon, The analysis of the fractional-order Navier-Stokes equations by a novel approach, J. Funct. Space., 2022 (2022), 8979447. https://doi.org/10.1155/2022/8979447 doi: 10.1155/2022/8979447
[12]	M. Alqhtani, K. M. Saad, W. Weera, W. M. Hamanah, Analysis of the fractional-order local Poisson equation in fractal porous media, Symmetry, 14 (2022), 1323. https://doi.org/10.3390/sym14071323 doi: 10.3390/sym14071323
[13]	M. Naeem, H. Rezazadeh, A. A. Khammash, S. Zaland, Analysis of the fuzzy fractional-order solitary wave solutions for the KdV equation in the sense of Caputo-Fabrizio derivative, J. Math., 2022 (2022), 3688916. https://doi.org/10.1155/2022/3688916 doi: 10.1155/2022/3688916
[14]	M. A. E. Abdelrahman, M. A. Sohaly, Solitary waves for the modified Korteweg-de Vries equation in deterministic case and random case, J. Phys. Math., 2017 (2017).
[15]	S. N. Rao, M. Khuddush, M. Singh, M. Z. Meetei, Infinite-time blowup and global solutions for a semilinear Klein-Gordan equation with logarithmic nonlinearity, Appl. Math. Sci. Eng., 31 (2023), 2270134. https://doi.org/10.1080/27690911.2023.2270134 doi: 10.1080/27690911.2023.2270134
[16]	J. H. He, X. H. Wu, Exp-function method for nonlinear wave equations, Chaos Soliton. Fract., 30 (2006), 700–708. https://doi.org/10.1016/J.CHAOS.2006.03.020 doi: 10.1016/J.CHAOS.2006.03.020
[17]	Y. Zhou, M. Wang, Y. Wang, Periodic wave solutions to a coupled KdV equations with variable coefficients, Phys. Lett. A, 308 (2003), 31–36. https://doi.org/10.1016/S0375-9601(02)01775-9 doi: 10.1016/S0375-9601(02)01775-9
[18]	J. H. He, Approximate solution of nonlinear differential equations with convolution product nonlinearities, Comput. Method. Appl. M., 167 (1998), 69–73. https://doi.org/10.1016/S0045-7825(98)00109-1 doi: 10.1016/S0045-7825(98)00109-1
[19]	N. Mahak, G. Akram, Exact solitary wave solutions by extended rational sine-cosine and extended rational sinh-cosh techniques, Phys. Scripta, 94 (2019), 115212. https://doi.org/10.1088/1402-4896/AB20F3 doi: 10.1088/1402-4896/AB20F3
[20]	N. A. Kudryashov, Simplest equation method to look for exact solutions of nonlinear differential equations, Chaos Soliton. Fract., 24 (2005), 1217–1231. https://doi.org/10.1016/J.CHAOS.2004.09.109 doi: 10.1016/J.CHAOS.2004.09.109
[21]	W. X. Ma, B. Fuchssteiner, Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation, Int. J. NonLin. Mech., 31 (1996), 329–338. https://doi.org/10.1016/0020-7462(95)00064-X doi: 10.1016/0020-7462(95)00064-X
[22]	C. Yan, A simple transformation for nonlinear waves, Phys. Lett. A, 224 (1996), 77–84. https://doi.org/10.1016/S0375-9601(96)00770-0 doi: 10.1016/S0375-9601(96)00770-0
[23]	N. A. Kudryashov, One method for finding exact solutions of nonlinear differential equations, Commun. Nonlinear Sci., 17 (2012), 2248–2253. https://doi.org/10.1016/J.CNSNS.2011.10.016 doi: 10.1016/J.CNSNS.2011.10.016
[24]	I. Onder, M. Ozisik, A. Secer, The soliton solutions of (2+ 1)-dimensional nonlinear two-coupled Maccari equation with complex structure via new Kudryashov scheme, New Trends Math. Sci., 10 (2022). https://doi.org/10.20852/ntmsci.2022.468 doi: 10.20852/ntmsci.2022.468
[25]	H. M. Baskonus, T. A. Sulaiman, H. Bulut, On the novel wave behaviors to the coupled nonlinear Maccari's system with complex structure, Optik, 131 (2017), 1036–1043. https://doi.org/10.1016/j.ijleo.2016.10.135 doi: 10.1016/j.ijleo.2016.10.135
[26]	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
[27]	D. Lu, Q. Shi, New Jacobi elliptic functions solutions for the combined KdV-mKdV equation, Int. J. Nonlinear Sci., 10 (2010), 320–325.

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