New Exact Non-Reducible Solutions for Generalized Zakharov-Kuznetsov Equation

Jafari, Mehdi

doi:10.22034/jdgaa.2024.711327

New Exact Non-Reducible Solutions for Generalized Zakharov-Kuznetsov Equation

Document Type : Original Article

Author

Mehdi Jafari

Department of Mathematics, Payame Noor University, PO BOX 19395-4697, Tehran, Iran.

10.22034/jdgaa.2024.711327

Abstract

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.

Keywords

Partially invariant solution

Generalized Zakharov-Kuznetsov equation

Optimal system

Similarity reduction