EVOLUTION AND STABILITY OF SELF-LOCALIZED MODES IN A NONLINEAR INHOMOGENEOUS CRYSTAL-LATTICE

The evolution and stability of self-localized modes in an inhomogeneou s crystal lattice are discussed. After establishing the basic equation s, appropriate time and space scales are introduced, together with a p ower threshold. A mathematical stability theory, based upon an average d Lagrangian analysis, concludes that the system is stable for any mas s defect, if the perturbation is symmetric. For asymmetric perturbatio ns, only single-peaked stationary states are stable. Finally, numerica l simulations are presented that not only support the theoretical work of the earlier sections but show clearly the evolution of the solutio ns from a range of input conditions.