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).