Uta Naether, R.A. Vicencio and Magnus Johansson
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.