Exact Solution for the Zakhrov-Kuzentsov Equation by Adomian Decomposition Method

Main Article Content

Fadlallah Mustafa Mosa
Eltayeb Abdellatif Mohamed Yousif

Abstract

The Zakharov-kuznetsov equation (ZK-equation) governs the behavior of weakly nonlinear ion-acoustic waves in plasma comprising cold ions and not isothermal electrons in the presence of a uniform magnetic field. This equation is a nonlinear equation. The main objective in this paper is to find an exact solution of ZK-equation using Adomain decomposition method. An exact solution of ZK(n,n,n) is derived by Adomain decomposition method. The solution of types ZK(2,2,2) and ZK(3,3,3) are presented in many examples to show the ability and efficiency of the method for ZK-equation. The solution is calculated in the form of convergent power series with easily computable components.

Keywords:
Zakhrov-Kuzentsov equation, Adomain decomposition method, analytical solution, Nonlinear partial differential equations.

Article Details

How to Cite
Mosa, F. M., & Yousif, E. A. M. (2020). Exact Solution for the Zakhrov-Kuzentsov Equation by Adomian Decomposition Method. Asian Research Journal of Mathematics, 16(4), 1-11. https://doi.org/10.9734/arjom/2020/v16i430182
Section
Original Research Article

References

Zakharov VE, Kuznetsov EA. On three dimensional solitons. Soviet physics. 1974;39:285-288.

Das GC, Sarma J, Talukder m. Dynamical aspects of various solitary waves and doible layers in dusty plasmas. phys. plasmas. 1998;5:63-69.

Mashaallah M, Maryam G. Variational homotopy perturbation method for the Zakharov- Kuznetsov equation. J. Math. and Statistics. 2010;6:425-430.

Susan M, Johnparkes. The stability of solitary wave solution to a modified zakharov kuznetsov equation. J. Plasma Physics. 2000;64:411-426.

Adomian G. Solving frontier problem of physics:The decomposition method. MA: Kluwer Academic Publishers Boston;1994.

Nuruddeen RI, Muhammad L, Nass AM, Sulaiman TA. A review of the integral transformsbased decomposition method and their applications in solving nonlinear PDEs. Palestine J.Math. 2018;7(1):262-280.

Nuruddeen RI. Elzaki decomposition method and its applications in solving linear and nonlinear schrodinger equations. Sohag J. Math. 2017;4(2):31-35.

MohyudDin ST, Yildrlm A. Exact solitary-wave solutions for the nonlinear dispersive K (2,2,1) and K (3,3,1) equations. J. king Saud University Science Elsevier. 2010;22:269274.

Korteweg DJ, devries G. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. philos Mag. 1895;(5)39,422-443.

Alaattin E, selcuk K. Travelling wave solutions for the generalized (2+1)-Dimensional ZKequation.
International J. of Nonlinear Science. 2009;4:428-434.

Nuruddeen RI, Suliman AK, Ali KK. Analytical investigtion of soliton solutions to three quantum zakharov-kuzentsov equations. Communications in Theoretical Physics; 2018.

Saeideh H, Alireza N, Ahmed H. Analytical solution for the Zakharov- Kuznetsov equation by differential transform method. International J. of Engineering and Natural Science. 2010;4:4.

Wazwaz AM. The modified decomposition method applied to unsteady flow of gas through aporous medium. Applied Mathematics and Computation. 2001;118:123132.

Abdou MA, Soliman AA. Variational iteration method for solving Burgers and coupled Burgers equations. Journal of computational and Applied mathematics. 2005;181(2):245-251.

Wazwaz AM. Acomputational approach to solutions of the Kadomtsev-petviashvili equation. Applied Mathematics and Computation. 2001;123(2:205-217.

Lesinc D. The decomposition method for initial value problems. Applied Mathematics and Computation. 2006;181 (1):206-213.

Wazwaz AM. Nonlinear dispersive special type of the ZK equation ZK (n,n) with compact and noncompact structures. Applied Mathematics and Computation. 2005;161(2):577-590.

Wazwaz AM. The modified decomposition method for analytic treatment of differential equation. Applied mathematics and computation. 2006;173(1):165-176.

Abassy TA. Improved Adomian Decomposition Method. Computers and Mathematics with Applications. 2010;59(1):42-54.