Peierls-Nabarro potential barrier for highly localized nonlinear modes

Abstract

We consider two types of strongly localized modes in discrete nonlinear lattices. Taking the lattice nonlinear Schr\"odinger (NLS) equation as a particular but rather fundamental example, we show that (1) the discreteness effects may be understood in the ``standard'' discrete NLS model as arising from an effective periodic potential similar to the Peierls-Nabarro (PN) barrier potential for kinks in the Frenkel-Kontorova model; (2) this PN potential vanishes in the completely integrable Ablowitz-Ladik variant of the NLS equation; and hence (3) the PN potential arises from the nonintegrability of the discrete physical models and determines the stability properties of the stationary localized modes.