NEW EXACT NON-REDUCIBLE SOLUTIONS FOR GENERALIZED ZAKHAROV-KUZNETSOV EQUATION

In this paper, we obtain new non-reducible exact solutions of generalized Zakharov-Kuznetsov equation by method of partially invariant solutions (PISs). PISs method is the generalization of the similarity reduction method. We focus on the case of PISs that have defect structure 1 and they obtained from three-dimensional subalgebras. For this purpose, we calculate the optimal system of 1, 2 and 3 dimensional subalgebras of the symmetry algebra for the equation. Also, it will be shown that these solutions are different from the group invariant solutions computed by the method of Lie
symmetry and their non-reducibility is proven. In this paper, we obtain new non-reducible exact solutions of generalized Zakharov-Kuznetsov equation by method of partially invariant solutions (PISs). PISs method is the generalization of the similarity reduction method. We focus on the case of PISs that have defect structure 1 and they obtained from three-dimensional subalgebras. For this purpose, we calculate the optimal system of 1, 2 and 3 dimensional subalgebras of the symmetry algebra for the equation. Also, it will be shown that these solutions are different from the group invariant solutions computed by the method of Lie symmetry and their non-reducibility is proven.