D.E. Pelinovsky and P.G. Kevrekidis
Discrete dark solitons in nonlinear Schrodinger lattices
Journal of Physics A: Mathematical General 41,
185206 (10pp) (2008)
Abstract:
We obtain new results on the stability of discrete dark
solitons bifurcating from the anticontinuum
limit of the discrete nonlinear Schršodinger equation,
following the analysis of our
previous paper [Physica D 212, 1-19 (2005)]. We derive
a criterion for stability or instability of
dark solitons from the limiting configuration of the
discrete dark soliton and confirm this criterion
numerically. We also develop detailed calculations of
the relevant eigenvalues for a number of
prototypical configurations and obtain very good
agreement of asymptotic predictions with the
numerical data.
Keywords:
discrete nonlinear Schrodinger equation, dark solitons,
existence and stability, approximation of eigenvalues