Analytical Solution For The Zakharov-Kuznetsov Equations By Differential Transform Method (original) (raw)

Exact solutions of modified Zakharov–Kuznetsov equation by the homogeneous balance method

Ain Shams Engineering Journal, 2014

In this article, the homogeneous balance method is used to construct exact traveling wave solutions for the modified Zakharov-Kuznetsov equation using the Riccati equation. This method is a powerful tool for obtaining exact traveling wave solutions of nonlinear evolution equation. Many exact traveling wave solutions of nonlinear modified Zakharov-Kuznetsov equation are constructed which contain soliton and periodic solutions. The results reveal that the method is very effective and simple.

New Explicit Solutions of the Generalized (2+ 1)-Dimensional Zakharov-Kuznetsov Equation

2012

ABSTRACT This paper studies the generalized (2+ 1)-dimensional Zakharov-Kuznetsov Equation using the (G'/G)-expand method, we obtain many new explicit solutions of the generalized (2+ 1)-dimensional Zakharov-Kuznetsov Equation, which include hyperbolic function solutions, trigonometric function solutions and rational function solutions and so on. Keywords: Zakharov-Kuznetsov Equation; The (G'/G)-Expand Method; Homogeneous Balance Principle; Explicit Solutions

Modified Kudryashov Method to Solve Generalized Kuramoto-Sivashinsky Equation

Symmetry, 2018

The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudryashov method for the new exact solutions. The modified Kudryashov method converts the given nonlinear partial differential equation to algebraic equations, as a result of various steps, which upon solving the so-obtained equation systems yields the analytical solution. By this way, various exact solutions including complex structures are found, and their behavior is drawn in the 2D plane by Maple to compare the uniqueness and wave traveling of the solutions.

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

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.