Abstract
This article investigates a nonlinear dispersive Zakharov-Kuznetsov ZK (3, 3, 3) equation. This equation governs the behavior of weakly nonlinear ion-acoustic waves in plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) are implemented for solving the ZK equation. Homotopy results were compared with results of Adomian decomposition Method (ADM). The results reveal that the HPM and VIM are very effective, convenient and quite accurate to systems of nonlinear partial differential equations.
Highlights
The investigation of the traveling wave solution plays an important role in nonlinear science
Rosenau and Hyman[1] introduced a class of partial differential equations (PDEs): are presented by Ismail and Taha[3] and Wazwaz[4] used a finite difference method and a finite element method to investigate the approximate solutions of k (2, 2) and k (3, 3) in Eq (1)
To understand the role of nonlinear dispersion in the formation of patterns in liquid drops, Yan[5] and Zhu[6] have introduced a family of fully Boussinesq equation B(m,n): K(m,n) :ut +a(um)x +(un )xxx = 0, m > 0,1< n ≤ 3 (1)
Summary
The investigation of the traveling wave solution plays an important role in nonlinear science. For values of m and n, the K (m , n ) equation has solitary waves which are compactly supported. The new solitary wave special solutions with compact support for the nonlinear dispersive K (m , n ) We apply the Homotopy-Perturbation Method (HPM)[9,10,11,12,13,14] and Variational Iteration Method (VIM) [15,16,17,18] to the ZK
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