In this research work, the Zakharov–Kuznetsov equation is solved analytically utilizing the similarity transformations approach via classical theory of Lie-group. At each stage, the similarity transformation technique (STM) lowers the number of independent variables by one. The STM is applied to Zakharov–Kuznetsov (ZK) equation and after successive application it reduces an ordinary differential equation. This can be solved further to get invariant solutions of the Zakharov–Kuznetsov equation. This research has the potential to solve Zakharov–Kuznetsov equation in a more general approach. Fluid mechanics, oceanography, optical fiber, fluid dynamics are all applications of the system.