Exact Solution for the Zakhrov-Kuzentsov Equation by Adomian Decomposition Method
Fadlallah Mustafa Mosa *
Department of Mathematics and Physics, Faculty of Education, University of Kassala, Kassala, Sudan.
Eltayeb Abdellatif Mohamed Yousif
Department of Applied Mathematics, College of Mathematical Science, University of Khartoum, Khartoum, Sudan.
*Author to whom correspondence should be addressed.
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.