Symmetry reductions of the ( 3 + 1 ) $(3+1)$ -dimensional modified Zakharov–Kuznetsov equation

Abstract

This paper is concerned with the symmetry reductions of the (3 + 1)-dimensional modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. The direct symmetry method is applied to determine the symmetry and the corresponding vector field. Then, the considered equation is reduced to lower-dimensional equations with the aid of the obtained symmetry. At last, some exact solutions of the modified Zakharov-Kuznetsov equation are found in terms of the lower-dimensional equations.

Lie symmetry reductions and conservation laws for fractional order coupled KdV system

“…The Lie symmetry technique is one of the most useful techniques to conclude to solutions of nonlinear FPDEs, generally, Lie symmetries might be used to reduce the order of the original equation (system of equations) as well as the number of independent variables [5][6][7][8][9][10][11].…”