He's variational method for the time-space fractal (3 + 1)-dimensional extended quantum Zakharov-Kuznetsov equation in plasma physics

Abstract

In this paper, we derive a new time-space fractal ()-dimensional extended quantum Zakharov-Kuznetsov (Z-K) equation based on He's fractal derivatives. Then He's variational method, together with the two-scale transform are implemented to seek the solitary wave solution of the fractal equation. The main advantage of the variational method is that it can reduce the order of the differential equation and make the equation more simple. The results show that the method is simple and effective, which is expected to shed a bright light on the study of the fractal nonlinear partial differential equations arising in physics.