**Commenced**in January 2007

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**Edition:**International

**Paper Count:**30843

##### Analytical Solution for the Zakharov-Kuznetsov Equations by Differential Transform Method

**Authors:**
Saeideh Hesam,
Alireza Nazemi,
Ahmad Haghbin

**Abstract:**

This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.

**Keywords:**
closed form solution,
differential transform method,
Zakharov-Kuznetsov equation

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1056593

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