Breathers in a Discrete Nonlinear Schr\"{o}dinger type Model : Exact Stability Results

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.