Title: Solitons in a modified discrete nonlinear Schroedinger equation,
Abstract: We study the bulk and surface nonlinear modes of the modified one-dimensional
discrete nonlinear Schroedinger (mDNLS) equation. A linear and a modulational
stability analysis of the lowest-order modes is carried out. While for the
fundamental bulk mode there is no power threshold, the fundamental surface mode
needs a minimum power level to exist. Examination of the time evolution of
discrete solitons in the limit of strongly localized modes, suggests ways to
manage the Peierls- Nabarro barrier, facilitating in this way a degree of
steering. The long-time propagation of an initially localized excitation shows
that, at long evolution times, nonlinear effects become negligible and as a
result, the propagation becomes ballistic. The similarity of all these results
to the ones obtained for the DNLS equation, points out to the robustness of the
discrete soliton phenomenology.