  We discuss a version the methodology for obtaining exact solutions of
nonlinear partial differential equations based on the possibility for use of:
(i) more than one simplest equation; (ii) relationship that contains as
particular cases the relationship used by Hirota \cite{hirota} and the
relationship used in the previous version of the methodology; (iii)
transformation of the solution that contains as particular case the possibility
of use of the Painleve expansion; (iv) more than one balance equation. The
discussed version of the methodology allows: (i) obtaining multi-soliton
solutions of nonlinear partial differential equations if such solutions do
exist; (ii) obtaining particular solutions of nonintegrable nonlinear partial
differential equations. Several examples for the application of the methodology
are discussed. Special attention is devoted to the use of the simplest equation
$f_\xi =n[f^{(n-1)/n} - f^{(n+1)/n}]$ where $n$ is a positive real number. This
simplest equation allows us to obtain exact solutions of nonlinear partial
differential equations containing fractional powers.
