  The method of simplest equation is applied for obtaining exact solitary
traveling-wave solutions of nonlinear partial differential equations that
contain monomials of odd and even grade with respect to participating
derivatives. The used simplest equation is $f_\xi^2 = n^2(f^2 -f^{(2n+2)/n})$.
The developed methodology is illustrated on two examples of classes of
nonlinear partial differential equations that contain: (i) only monomials of
odd grade with respect to participating derivatives; (ii) only monomials of
even grade with respect to participating derivatives. The obtained solitary
wave solution for the case (i) contains as particular cases the solitary wave
solutions of Korteweg-deVries equation and of a version of the modified
Korteweg-deVries equation.
