Dynamic wave solutions for (2+1)-dimensional DJKM equation in plasma physics

Ahmed A. Gaber; Abdul-Majid Wazwaz; Ahmed A. Gaber; Abdul-Majid Wazwaz

doi:10.3934/math.2024296

AIMS Mathematics

2024, Volume 9, Issue 3: 6060-6072. doi: 10.3934/math.2024296

Previous Article Next Article

Research article

Dynamic wave solutions for (2+1)-dimensional DJKM equation in plasma physics

Ahmed A. Gaber ^{1
,
,},
Abdul-Majid Wazwaz ²

1.
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, 11952, Suadi Arab
2.
Department of Mathematics, Saint Xavier University, Chicago, IL USA 60655

Received: 30 November 2023 Revised: 09 January 2024 Accepted: 18 January 2024 Published: 01 February 2024
MSC : 34A06, 35A09, 35A24

In this paper, we attempt to obtain exact and novel solutions for Date-Jimbo-Kashiwara-Miwa equation (DJKM) via two different techniques: Lie symmetry analysis and generalized Kudryashov method (GKM). This equation has applications in plasma physics, fluid mechanics, and other fields. The Lie symmetry method is applied to reduce the governing equation to five different ordinary differential equations (ODEs). GKM is used to obtain general and various periodic solutions. These solutions have different behaviors such as kink wave, anti-kink wave, double soliton, and single wave solution. The physical behavior of the solutions was reviewed through 2-D and 3-D graphs.
- Lie symmetry analysis,
- generalization Kudryashov method,
- Date-Jimbo-Kashiwara-Miwa equation,
- exact solutions
Citation: Ahmed A. Gaber, Abdul-Majid Wazwaz. Dynamic wave solutions for (2+1)-dimensional DJKM equation in plasma physics[J]. AIMS Mathematics, 2024, 9(3): 6060-6072. doi: 10.3934/math.2024296

Related Papers:

Abstract

In this paper, we attempt to obtain exact and novel solutions for Date-Jimbo-Kashiwara-Miwa equation (DJKM) via two different techniques: Lie symmetry analysis and generalized Kudryashov method (GKM). This equation has applications in plasma physics, fluid mechanics, and other fields. The Lie symmetry method is applied to reduce the governing equation to five different ordinary differential equations (ODEs). GKM is used to obtain general and various periodic solutions. These solutions have different behaviors such as kink wave, anti-kink wave, double soliton, and single wave solution. The physical behavior of the solutions was reviewed through 2-D and 3-D graphs.

References

[1]	A. Gaber, A. Wazwaz, Symmetries and dynamic wave solutions for (3+1)-dimensional potential Calogero-Bogoyavlenskii-Schiff equation, J. Ocean Eng. Sci., in press. http://dx.doi.org/10.1016/j.joes.2022.05.018
[2]	A. Gaber, Solitary and periodic wave solutions of (2+1)-dimensions of dispersive long wave equations on shallow waters, J. Ocean Eng. Sci., 6 (2021), 292–298. http://dx.doi.org/10.1016/j.joes.2021.02.002 doi: 10.1016/j.joes.2021.02.002
[3]	A. Gaber, F. Alsharari, S. Kumar, Some closed-form solutions, conservation laws, and various solitary waves to the (2+1)-D potential B-K equation via Lie symmetry approach, Int. J. Mod. Phys. B, 36 (2022), 2250117. http://dx.doi.org/10.1142/S021797922250117X doi: 10.1142/S021797922250117X
[4]	Z. Zhao, L. He, Lie symmetry, nonlocal symmetry analysis, and interaction of solutions of a (2+1)-dimensional Kdv-Mkdv equation, Theor. Math. Phys., 206 (2021), 142–162. http://dx.doi.org/10.1134/S0040577921020033 doi: 10.1134/S0040577921020033
[5]	M. Ablowitz, D. Kaup, A. Newell, Coherent pulse propagation, a dispersive, irreversible phenomenon, J. Math. Phys., 15 (1974), 1852–1858. http://dx.doi.org/10.1063/1.1666551
[6]	A. Wazwaz, The extended tanh method for new compact and noncompact solutions for the KP-BBM and the ZK-BBM equations, Chaos Soliton. Fract., 38 (2008), 1505–1516. http://dx.doi.org/10.1016/j.chaos.2007.01.135 doi: 10.1016/j.chaos.2007.01.135
[7]	Z. Dimitrova, K. Vitanov, Homogeneous balance method and auxiliary equation method as particular cases of simple equations method, AIP Conf. Proc., 2321 (2021), 030004. http://dx.doi.org/10.1063/5.0043070 doi: 10.1063/5.0043070
[8]	K. Khan, A. Ali, M. Irfan, Z. Khan, Solitary wave solutions in time-fractional Korteweg-de Vries equations with power law kernel, AIMS Mathematics, 8 (2023), 792–814. http://dx.doi.org/10.3934/math.2023039 doi: 10.3934/math.2023039
[9]	M. Mamun Miah, H. Shahadat Ali, M. Ali Akbar, A. Seadawy, New applications of the two variable (G$^{\prime}$/G, 1/G)-expansion method for closed form traveling wave solutions of integro-differential equations, J. Ocean Eng. Sci., 4 (2019), 132–143. http://dx.doi.org/10.1016/j.joes.2019.03.001 doi: 10.1016/j.joes.2019.03.001
[10]	M. Shakeel, Attaullah, N. Ali Shah, J. Chung, Modified exp-function method to find exact solutions of microtubules nonlinear dynamics models, Symmetry, 15 (2023), 360. http://dx.doi.org/10.3390/sym15020360 doi: 10.3390/sym15020360
[11]	A. Gaber, A. Wazwaz, M. Mousa, Similarity reductions and new exact solutions for (3+1)-dimensional B-B equation, Mod. Phys. Lett. B, 38 (2024), 2350243. http://dx.doi.org/10.1142/S0217984923502433 doi: 10.1142/S0217984923502433
[12]	S. Kumar, K. Nisar, M. Niwas, On the dynamics of exact solutions to a (3+1)-dimensional YTSF equation emerging in shallow sea waves: Lie symmetry analysis and generalized Kudryashov method, Results Phys., 48 (2023), 106432. http://dx.doi.org/10.1016/j.rinp.2023.106432 doi: 10.1016/j.rinp.2023.106432
[13]	A. Gaber, A. Aljohani, A. Ebaid, J. Tenreiro Machado, The generalized Kudryashov method for nonlinear space-time fractional partial differential equations of Burgers type, Nonlinear Dyn., 95 (2019), 361–368. http://dx.doi.org/10.1007/s11071-018-4568-4 doi: 10.1007/s11071-018-4568-4
[14]	K. Bibi, K. Ahmad, New exact solutions of date Jimbo Kashiwara Miwa equation using Lie symmetry groups, Math. Probl. Eng., 2021 (2021), 5533983. http://dx.doi.org/10.1155/2021/5533983 doi: 10.1155/2021/5533983
[15]	N. Sajid, G. Akram, The application of the exp(-$\Phi$($\xi $))-expansion method for finding the exact solutions of two integrable equations, Math. Probl. Eng., 2018 (2018), 5191736. http://dx.doi.org/10.1155/2018/5191736 doi: 10.1155/2018/5191736
[16]	G. Akram, N. Sajid, M. Abbas, Y. Hamed, K. Abualnaja, Optical solutions of the Date-Jimbo-Kashiwara-Miwa equation via the extended direct algebraic method, J. Math., 2021 (2021), 5591016. http://dx.doi.org/10.1155/2021/5591016 doi: 10.1155/2021/5591016
[17]	A. Rashed, S. Mabrouk, A. Wazwaz, Forward scattering for non-linear wave propagation in (3+1)-dimensional Jimbo-Miwa equation using singular manifold and group transformation methods, Wave. Random Complex, 32 (2022), 663–675. http://dx.doi.org/10.1080/17455030.2020.1795303 doi: 10.1080/17455030.2020.1795303
[18]	A. Halder, A. Paliathanasis, R. Seshadri, P. Leach, Lie symmetry analysis and similarity solutions for the Jimbo-Miwa equation and generalisations, Int. J. Nonlin. Sci. Num., 21 (2020), 767–779. http://dx.doi.org/10.1515/ijnsns-2019-0164 doi: 10.1515/ijnsns-2019-0164
[19]	A. Wazwaz, New (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equations with constant and time-dependent coefficients: Painlevé integrability, Phys. Lett. A, 384 (2020), 126787. http://dx.doi.org/10.1016/j.physleta.2020.126787 doi: 10.1016/j.physleta.2020.126787
[20]	S. Kumar, K. Nisar, M. Niwas, On the dynamics of exact solutions to a (3+1)-dimensional YTSF equation emerging in shallow sea waves: Lie symmetry analysis and generalized Kudryashov method, Results Phys., 48 (2023), 106432. http://dx.doi.org/10.1016/j.rinp.2023.106432 doi: 10.1016/j.rinp.2023.106432
[21]	M. El-Sayed, G. Moatimid, M. Moussa, R. El-Shiekh, F. El-Shiekh, A. El-Satar, A study of integrability and symmetry for the (p+1)th Boltzmann equation via Painlevé analysis and Lie-group method, Math. Method. Appl. Sci., 38 (2015), 3670–3677. http://dx.doi.org/10.1002/mma.3307 doi: 10.1002/mma.3307
[22]	S. Ray, Vinita, Lie symmetry analysis, symmetry reductions with exact solutions, and conservation laws of (2+1)-dimensional Bogoyavlenskii-Schieff equation of higher order in plasma physics, Math. Method. Appl. Sci., 43 (2020), 5850–5859. http://dx.doi.org/10.1002/mma.6328 doi: 10.1002/mma.6328
[23]	Z. Zhao, Bäcklund transformations, nonlocal symmetry and exact solutions of a generalized (2+1)-dimensional Korteweg-de Vries equation, Chinese J. Phys., 73 (2021), 695–705. http://dx.doi.org/10.1016/j.cjph.2021.07.026 doi: 10.1016/j.cjph.2021.07.026
[24]	S. Tian, M. Xu, T. Zhang, A symmetry-preserving difference scheme and analytical solutions of a generalized higher-order beam equation, Proc. R. Soc. A, 477 (2021), 20210455. http://dx.doi.org/10.1098/rspa.2021.0455 doi: 10.1098/rspa.2021.0455

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)