Bifurcation analysis of the localized modes dynamics in lattices with saturable nonlinearity

The dynamics of localized modes in discrete media with saturable nonlinearity are investigated. The stability of stationary bright solitons is discussed from the view point of the energy minimum principle and mapping analysis. Due to the cascade saturation mechanism, a bifurcation from trapped to transversely moving localized mode is found for particular values of high power. The bifurcation coincides with the existence of the (almost) perfect separatrix in the corresponding area-preserving map. In addition, the definition of the Peierls–Nabarro effective potential is reconsidered.