Breathers in a Discrete Nonlinear Schrödinger type Model : Exact Stability Results

Abstract

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.

4 pages, 9 figures and 8 references

References in corpus (2)

• Observation of breathers in Josephson ladders
• Growth and decay of discrete nonlinear Schroedinger breathers interacting with internal modes or standing-wave phonons

Cited by in corpus (1)

• Standing Waves in a Non-linear 1D Lattice : Floquet Multipliers, Krein Signatures, and Stability