In this article, we employ the Mikhailov–Novikov–Wang integrable equation (MNWIE) appearing by means of the perturbatives symmetry approach to the rating of integrable non-evolutionary PDEs. The new exact soliton solutions of this equation which were not achieved before have been realized for the first time in the framework of the (G′/G)-expansion method. In the same vein and parallel, the corresponding numerical solutions of this equation have been established using the variational iterationmethod (VIM).