Some new invariant solutions of nonlinear fifth order partial differential equation via Lie approach

In this paper, the classical Lie symmetry analysis of ( 1 + 3 ) dimensional perturbed Zakharov–Kuznetsov (pZK) equation has been studied. We present a thorough classification of Lie point symmetries for pZK equation. Additionally, we offer the corresponding interpretation of symmetry transformation groups. Based on Lie point symmetries, many reductions, and numerous group invariant solutions have been constructed for the pZK equation. These constructed new closed form analytical solutions which are very important in the field of physics and applied science. For many interesting invariant solutions, and figures illustrates the properties. The solutions discussed are essential for advancing our understanding of wave dynamics in plasma physics. Furthermore, to demonstrate our conclusions directly, we present the corresponding invariant solutions to this equation using the Lie approach.