Modified method of simplest equation for obtaining exact solutions of nonlinear partial differential equations: past and present

We present a short review of the evolution of the methodology of the Method of simplest equation for obtaining exact particular solutions of nonlinear partial differential equations (NPDEs) and the recent extension of a version of this methodology called Modified method of simplest equation. This extension makes the methodology capable to lead to solutions of nonlinear partial differential equations that are more complicated than a single solitary wave.