Lie symmetries, conservation laws, reductions, and new exact solutions of the extended form of the \((2+1)\) -dimensional generalized Zakharov–Kuznetsov (ZK) equation are studied. This generalized ZK model includes three arbitrary exponents m, n and k in the nonlinear terms. The Lie algebra for the generalized ZK model is four dimensional. Conservation laws are derived using the multiplier method and five cases arise under different restrictions on the parameters m, n and k of the model. Lie symmetries associated with the conserved vectors are determined for each case. Furthermore, several reductions and new exact solutions of ZK equation are established using the generalized double reduction theory. These solutions advance the analysis of nonlinear dynamics in physical systems including plasmas, shallow water flows, and other dispersive media.
