## Abstract and Applied Analysis

### Some Reduction and Exact Solutions of a Higher-Dimensional Equation

#### Abstract

The conservation laws of the $(3+1)$-dimensional Zakharov-Kuznetsov equation were obtained using Noether’s theorem after an interesting substitution $u={v}_{x}$ to the equation. Then, with the aid of an obtained conservation law, the generalized double reduction theorem was applied to this equation. It can be verified that the reduced equation is a second order nonlinear ODE. Finally, some exact solutions of the Zakharov-Kuznetsov equation were constructed after solving the reduced equation.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 597470, 9 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412607185

Digital Object Identifier
doi:10.1155/2014/597470

Mathematical Reviews number (MathSciNet)
MR3216066

Zentralblatt MATH identifier
07022689

#### Citation

Wang, Guangming; Han, Zhong. Some Reduction and Exact Solutions of a Higher-Dimensional Equation. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 597470, 9 pages. doi:10.1155/2014/597470. https://projecteuclid.org/euclid.aaa/1412607185

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