Group analysis of the modified generalized Vakhnenko equation

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.

► 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.