Stability analysis for Zakharov–Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma

The Zakharov–Kuznetsov (ZK) equation is an isotropic nonlinear evolution equation, first derived for weakly nonlinear ion-acoustic waves in a strongly magnetized lossless plasma in two dimensions. In the present study, by applying the extended direct algebraic method, we found the electric field potential, electric field and magnetic field in the form of traveling wave solutions for the two-dimensional ZK equation. The solutions for the ZK equation are obtained precisely and the efficiency of the method can be demonstrated. The stability of these solutions and the movement role of the waves are analyzed by making graphs of the exact solutions.