Compactification tuning for nonlinear localized modes in sawtooth lattices

Uta Naether, R.A. Vicencio and Magnus Johansson
ARXIV (2015)


We discuss the properties of nonlinear localized modes in sawtooth lattices, in the
framework of a discrete nonlinear Schr” odinger model with general on-site nonlinearity.
Analytic conditions for existence of exact compact three-site solutions are obtained, and
explicitly illustrated for the cases of power-law (cubic) and saturable nonlinearities. These
nonlinear compact modes appear as continuations of linear compact modes belonging to a
flat dispersion band. While for the linear system a compact mode exists only for one.