Abstract and Applied Analysis

Some Reduction and Exact Solutions of a Higher-Dimensional Equation

Guangming Wang and Zhong Han

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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.

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

First available in Project Euclid: 6 October 2014

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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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