Some Reduction and Exact Solutions of a Higher-Dimensional Equation

Abstract EN

The conservation laws of the (3+1)-dimensional Zakharov-Kuznetsov equation wereobtained using Noether’s theorem after an interesting substitution u=vx to theequation.

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 theZakharov-Kuznetsov equation were constructed after solving the reduced equation.