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

The evolution and stability of self-localized modes in an inhomogeneous crystal lattice are discussed. After establishing the basic equations, appropriate time and space scales are introduced, together with a power threshold. A mathematical stability theory, based upon an averaged Lagrangian analysis, concludes that the system is stable for any mass defect, if the perturbation is symmetric. For asymmetric perturbations, only single-peaked stationary states are stable. Finally, numerical simulations are presented that not only support the theoretical work of the earlier sections but show clearly the evolution of the solutions from a range of input conditions.