The conservation laws of the -dimensional Zakharov-Kuznetsov equation were obtained using Noether’s theorem after an interesting substitution 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.
Guangming Wang. Zhong Han. "Some Reduction and Exact Solutions of a Higher-Dimensional Equation." Abstr. Appl. Anal. 2014 (SI31) 1 - 9, 2014. https://doi.org/10.1155/2014/597470