  Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are
approximated by equations of the discrete nonlinear Schrodinger type. We show
how to justify this approximation by two methods, which have been very popular
in the recent literature. The first method relies on a priori energy estimates
and multi-scale decompositions. The second method is based on a resonant normal
form theorem. We show that although the two methods are different in the
implementation, they produce equivalent results as the end product. We also
discuss applications of the discrete nonlinear Schrodinger equation in the
context of existence and stability of breathers of the Klein--Gordon lattice.
