  We consider the problem of the existence of a dynamical barrier of ``mass''
that needs to be excited on a lattice site to lead to the formation and
subsequent persistence of localized modes for a nonlinear Schrodinger lattice.
We contrast the existence of a dynamical barrier with its absence in the static
theory of localized modes in one spatial dimension. We suggest an energetic
criterion that provides a sufficient, but not necessary, condition on the
amplitude of a single-site initial condition required to form a solitary wave.
We show that this effect is not one-dimensional by considering its
two-dimensional analog. The existence of a sufficient condition for the
excitation of localized modes in the non-integrable, discrete, nonlinear
Schrodinger equation is compared to the dynamics of excitations in the
integrable, both discrete and continuum, version of the nonlinear Schrodinger
equation.

Pattern Formation and Solitons