Symmetry reduction, conservation laws and acoustic wave solutions for the extended Zakharov–Kuznetsov dynamical model arising in a dust plasma

In this article, we consider the extended Zakharov–Kuznetsov (EZK) equation, which describes the nonlinear plasma dust acoustic waves (DAWs) in a magnetized dusty plasma. Dusty plasmas consist of three components: electrons, highly negatively charged dust grains, and two-temperature ions (low-temperature ions and high-temperature ions). We study the Lie symmetries, reductions, conservation laws and new exact solutions of EZK equations. Conservation laws for EZK equation is derived by applying the new conservation theorem of Ibragimov. Similarity solution for EZK equation will be obtained using Lie symmetry method. We find the Lie symmetries group of EZK equation, using similarity variables, get reduction equation, solving the reduction equations and then get the similarity solution. Solitary wave solutions of the EZK equation are derived from the reduction equation. Thus, some new exact explicit solutions of the EZK equation are obtained. •We consider Nonlinear evolution dynamical equations.•Symmetry reduction, conservation laws and acoustic wave solutions are found.•We applied hydrodynamic mathematical methods.•Extended Zakharov–Kuznetsov dynamical model arising in a dust plasma.