Some Reduction and Exact Solutions of a Higher-Dimensional Equation - Guangming Wang; Zhong Han (Abstract and Applied Analysis)
The conservation laws of the (3+1)-dimensional Zakharov-Kuznetsov equation were obtained using Noether’s theorem after an interesting substitution u=vx 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.