SYMMETRY SCHEME OF THE TIME FRACTIONAL (3+1)(3+1)-DIMENSIONAL MODIFIED EXTENDED ZAKHAROV–KUZNETSOV EQUATION IN PLASMA PHYSICS
Abstract
Higher-dimensional nonlinear models can describe more complex evolutionary mechanisms. In this paper, we considered the time fractional (3+1)(3+1)-dimensional modified extended Zakharov–Kuznetsov equation with the sense of the Riemann–Liouville fractional derivative in plasma physics. In the first place, the existence of symmetry of this studied equation through the symmetry scheme was proved. Then, the optimal system to the time fractional (3+1)(3+1)-dimensional modified extended Zakharov–Kuznetsov equation was also constructed. Subsequently, the time fractional higher-dimensional equation was reduced into the lower-dimensional fractional differential equation with the help of the Erdélyi–Kober fractional operators. Last, some conservation laws by using a new conservation theorem were also given. These novel results provide a window for us to discover this high-dimensional nonlinear equation.
