Group analysis of the modified generalized Vakhnenko equation

► Lie group analysis is applied to the modified generalized Vakhnenko equation. ► Similarity reductions and new exact solutions are derived. ► Numerical solutions are also obtained by using a group preserving numerical algorithm. In this paper the Lie symmetry group, the corresponding symmetry reductions and invariant solutions of the modified generalized Vakhnenko equation are determined. Moreover a numerical algorithm that is based on a Lie symmetry group preserving scheme is applied to the ordinary differential equations obtained by symmetry reduction.