Intraband discrete breathers in disordered nonlinear systems. II: Localization
[For part I see the authors, ibid. 130, No.~3-4, 155-186 (1999; Zbl 0943.70016).] From the summary: We find spatially localized, time-periodic solutions (discrete breathers or DBs) in disordered nonlinear systems with frequency inside the linear phonon spectrum under conditions that strictly prohibit their existence in their periodic counterparts. For that purpose, we develop a new in situ method for the calculation of these solutions which does not make use of any continuation from an anticontinuous limit. Using this method, we demonstrate that intraband localized modes (intraband discrete breathers or IDBs) at a given site with frequencies inside the discrete linear spectrum do exist, provided these frequencies do not belong to forbidden resonance gaps. Since there is a dense set of resonant frequencies, we illustrate numerically that the localized DBs exist provided that their frequencies belong to fat Cantor sets (i.e., with a finite measure). Such a set contains as accumulation points the linear frequency of the normal mode at the occupied site. We check that many of these solutions are linearly stable, and conjecture that their frequency belongs to another smaller fat Cantor set.
scientific article; zbMATH DE number 1515736