  Exact stability analysis of 1-site breathers in an NLS type model (ref. [4],
see below) indicates destabilisation through a growth rate becoming positive as
a stability border is crossed, while above a critical spatial decay rate
($\lambda_c$) the breather is always unstable. Similar analysis on 2-site
breathers with phase difference $\pi$ (see below) indicates destabilisation
through {\it Krein collision} of a pair of growth rates. All eigenmodes can be
exactly calculated and conform to numerical estimates.
