Solutions of Generalized Fractional Perturbed Zakharov-Kuznetsov Equation Arising in a Magnetized Dusty Plasma

Authors

  • Lanre Akinyemi Prairie View A&M University

DOI:

https://doi.org/10.31349/RevMexFis.67.060703

Keywords:

Perturbed (3 1)-dimensional Zakharov–Kuznetsov equation, Conformable derivative, Sub-equation method, Riccati equation, Mathematical physics

Abstract

The generalized fractional perturbed (3+1)-dimensional Zakharov–Kuznetsov (PZK) equation which appear in the magnetized two-ion-temperature dusty plasma and quantum physics is considered. The sub-equation method in the conformable sense is proposed to obtained closed-form analytical solutions to this equation. The newly solutions obtained by the proposed method are kink-shape, multi-soliton, solitary wave, bell-shaped solitons, and periodic solutions that are substantial in the field of mathematical physics and can be of relevance in the field of plasma physics, also for future research.

Author Biography

Lanre Akinyemi, Prairie View A&M University

Department of Mathematics

References

Yan, Z.: Abundant families of Jacobi elliptic function solutions of the (2+1)-dimensional integrable Davey–Stewartson-type equation via a new method. Chaos Soliton Fract. 18(2), 299-309 (2003)

Adomian, G.: Solving Frontier Problems of Physics: The Decomposition Method. Kluwer, (1994)

Wazwaz, A.M.: The sine–cosine method for obtaining solutions with compact and noncompact structures. Appl. Math. Comput. 159(2), 559–576 (2004)

Wazwaz, A.M.: A sine–cosine method for handling nonlinear wave equations. Math. Comput. Model. 40(5–6), 499–508 (2004)

El-Ganaini, S.: Solutions of some class of nonlinear PDEs in mathematical physics. J. Egypt. Math. Soc. 24, 214-219 (2016)

El-Ganaini, S.I.A.: Traveling wave solutions to the generalized Pochhammer–Chree (PC) equations using the first integral method. Math. Probl. Eng. 2011, 1-13 (2011)

Das, S.: Analytical solution of a fractional diffusion equation by variational iteration method. Comput. Math. Appl. 57, 483-487 (2009)

He, J.H.: Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Meth. Appl. Mech. Eng. 167, 57-68 (1998)

Fan, E.: Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277(4-5), 212-218 (2000)

El-Wakil, S.A., Abdou, M.A.: New exact travelling wave solutions using modified extended tanh-function method. Chaos Soliton Fract. 31(4), 840-852 (2007)

Akinyemi, L.: q-Homotopy analysis method for solving the seventh-order time-fractional Lax's Korteweg–de Vries and Sawada–Kotera equations. Comp. Appl. Math. 38(4), 1-22 (2019)

Akinyemi, L., Iyiola, O.S., Akpan, U.: Iterative methods for solving fourth- and sixth order time-fractional Cahn-Hillard equation. Math. Meth. Appl. Sci. 43(7), 4050–4074 (2020). https://doi.org/10.1002/mma.6173

El-Tawil, M.A., Huseen, S.N.: The Q-homotopy analysis method (q-HAM). Int. J. Appl. Math. Mech. 8(15), 51-75 (2012)

He, J.H., Wu, X.H.: Exp-function method for nonlinear wave equations. Chaos Solitons Fract. 30(3), 700–708 (2006)

Yusufoglu, E.: New solitary solutions for the MBBM equations using Exp-function method. Phys. Letters A 372, 442–446 (2008)

Zhang, S.: Application of Exp-function method to high-dimensional nonlinear evolution equation. Chaos, Solitons Fract. 38(1), 270–276 (2008)

Akinyemi, L., Huseen, S.N.: A powerful approach to study the new modified coupled Korteweg–de Vries system. Math. Comput. Simul. 177, 556-567 (2020). https://doi.org/10.1016/j.matcom.2020.05.021

Akinyemi, L. Iyiola, O.S.: A reliable technique to study nonlinear time-fractional coupled Korteweg-de Vries equations. Adv. Differ. Equ. 2020(169), 1-27 (2020). https://doi.org/10.1186/s13662-020-02625-w

Kumara, D., Singha, J., Baleanu, D.: A new analysis for fractional model of regularized long-wave equation arising in ion acoustic plasma waves. Math. Meth. Appl. Sci. 40, 5642-5653 (2017)

Malfliet, W., Hereman, W.: The tanh method: I. Exact solutions of nonlinear evolution and wave equations. Phys. Scripta 54, 563-568 (1996)

Fan E.: Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics. Chaos Solitons Fract. 16(5), 819-839 (2003)

Wang, M., Li, X.: Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation. Chaos Solitons Fract. 24(5), 1257-1268 (2005)

Wazwaz, A.M.: The tanh method for travelling wave solutions of nonlinear equations. Appl. Math. Comput. 154(3), 713-723 (2004)

He, J.H.: Homotopy perturbation technique. Comput. Meth. Appl. Mech. Eng. 178, 257-62 (1999)

Wang, M., Li, X., Zhang, J.: The G'/G-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Letters A 372(4), 417–423 (2008)

Bekir, A.: Application of the G'/G-expansion method for nonlinear evolution equations. Phys. Letters A 372(19), 3400–3406 (2008)

Keskin, Y., Oturanc, G.: Reduced differential transform method: a new approach to fractional partial differential equations. Nonlinear Sci. Lett. A 1, 61-72 (2010)

Akinyemi, L.: A fractional analysis of Noyes–Field model for the nonlinear Belousov–Zhabotinsky reaction. Comp. Appl. Math. 39, 1-34 (2020). https://doi.org/10.1007/s40314-020-01212-9

Fan, E.G., Zhang, Q.H.: A note on the homogeneous balance method. Phys. Lett. A 246, 403-406 (1998)

Wang, M.L.: Exact solutions for a compound KdV-Burgers equation. Phys. Lett. A 213, 279-287 (1996)

Vakhnenko, V.O., Parkes, E.J., Morrison, A.J.: A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation. Chaos Soliton Fract. 17(4), 683-692 (2003)

Akinyemi, L., Iyiola, O.S.: Exact and approximate solutions of time-fractional models arising from physics via Shehu transform. Math. Meth. Appl. Sci. 1–23 (2020). https://doi.org/10.1002/mma.6484

Alagesan, T., Uthayakumar, A., Porsezian, K., Painlev analysis and Backlund transformation for a three-dimensional Kadomtsev-Petviashvili equation. Chaos Solitons Fract. 8, 893-895 (1997)

Liao, S.J.: On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 147(2), 499-513 (2004)

Liao,S.J.: An approximate solution technique not depending on small parameters: a special example. Intern. J. Non-linear Mech. 30(3), 371-380 (1995)

Tasbozan, O., Çenesiz, Y., Kurt, A.: New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method. The European Physical Journal Plus 131(7), 1-14 (2016)

Tasbozan, O., Kurt, A., Tozar, A.: New optical solutions of complex Ginzburg–Landau equation arising in semiconductor lasers. Appl. Phys. B 125(6), 1-12 (2019)

Alquran, M., Al-Khaled, K., Chattopadhyay, J.: Analytical solutions of fractional population diffusion model: residual power series. Nonlinear Studies 22(1), 31-9 (2015)

Senol, M., Iyiola, O.S., Daei Kasmaei, H., Akinyemi, L.: Efficient analytical techniques for solving time-fractional nonlinear coupled Jaulent-Miodek system with energy-dependent Schr"odinger potential. Adv. Differ. Equ. 2019, 1-21 (2019)

Senol, M.: Analytical and approximate solutions of (2+ 1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation. Commun. Theor. Phys. 72(5), 1-11 (2020)

Senol, M., Dolapci, I.T.: On the Perturbation–Iteration Algorithm for fractional differential equations. Journal of King Saud University-Science 28(1), 69-74 (2016)

Senol, M., Atpinar, S., Zararsiz, Z., Salahshour, S., Ahmadian, A.: Approximate solution of time-fractional fuzzy partial differential equations. Comput. Appl. Math. 38(1), 1-18 (2019)

Seadawy, A.R., Lu, D.: Ion acoustic solitary wave solutions of three-dimensional nonlinear extended Zakharov-Kuznetsov dynamical equation in a magnetized two-ion-temperature dusty plasma. Results Phys. 6, 590-593 (2016)

Lu, D., Seadawy, A.R., Arshad, M., Wang, J.: New solitary wave solutions of (3+1)-dimensional nonlinear extended Zakharov–Kuznetsov and modified KdV–Zakharov–Kuznetsov equations and their applications. Results Phys. 7, 899–909 (2017). https://doi.org/10.1016/j.rinp.2017.02.002

Zhen, H., Tian, B., Wang, Y., Sun, W., Liu, L.: Soliton solutions and chaotic motion of the extended Zakharov-Kuznetsov equations in a magnetized two-ion-temperature dusty plasma. Phys Plasma 21, 073709 (2014)

Kumar, S., Kumar, D.: Solitary wave solutions of (3 + 1)-dimensional extended Zakharov–Kuznetsov equation by Lie symmetry approach. Comput. Math. Appl. 77, 2096–2113 (2019)

Mace, R.L., Hellberg, M.A.: The Korteweg–de Vries–Zakharov–Kuznetsov equation for electron-acoustic waves. Physics of Plasmas. 8(6), 2649–2656 2001

Elwakil, S.A., El-Shewy, E.K., Abdelwahed, H.G.: Solution of the perturbed Zakharov–Kuznetsov (ZK) equation describing electron-acoustic solitary waves in a magnetized plasma. Chin. J. Phys. 49(3), 732–744 (2011)

Ali, M.N., Seadawy, A.R., Husnine, S.M.: Lie point symmetries exact solutions and conservation laws of perturbed Zakharov–Kuznetsov equation with higher-order dispersion term. Mod. Phys. Lett. A 34, 1950027 (2019)

Kumar, D., Kumar, S.: Solitary wave solutions of PZK equation using lie point symmetries. Eur. Phys. J. Plus 135(2), 1-19 (2020)

Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65-70 (2014)

Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)

Zhang, S., Zhang, H.Q.: Fractional sub-equation method and its applications to nonlinear fractional PDEs. Phys. Lett. A 375(7), 1069-1073 (2011)

Akinyemi, L., Senol, M., Iyiola, O.S.: Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method. Math. Comput. Simul. 182, 211-233 (2020). https://doi.org/10.1016/j.matcom.2020.10.017

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Published

2021-11-01

How to Cite

[1]
L. Akinyemi, “Solutions of Generalized Fractional Perturbed Zakharov-Kuznetsov Equation Arising in a Magnetized Dusty Plasma”, Rev. Mex. Fís., vol. 67, no. 6 Nov-Dec, pp. 060703 1–, Nov. 2021.

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Section

07 Gravitation, Mathematical Physics and Field Theory