In this work, we study a generalised (2 + 1) equation of the Zakharov–Kuznetsov (ZK) (m , n , k) equation involving three arbitrary functions. From the point of view of the Lie symmetry theory, we have derived all Lie symmetries of this equation depending on the arbitrary functions. Line soliton solutions have also been obtained. Moreover, we study the low-order conservation laws by applying the multiplier method. This family of equations is rich in Lie symmetries and conservation laws. Finally, when the equation is expressed in potential form, it admits a variational structure in the case when two of the arbitrary functions are linear. In addition, the corresponding Hamiltonian formulation is presented. [ABSTRACT FROM AUTHOR]