  We apply the method of simplest equation 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. We consider first the general case of presence of monomials of the
both (odd and even) grades and then turn to the two particular cases of
nonlinear equations that contain only monomials of odd grade or only monomials
of even grade. The methodology is illustrated by numerous examples.
