Impurity modes in disordered non-linear lattices

Localized standing waves (impurity modes) centered on disorders of non-linear lattices of infinite spatial extent are analyzed. In contrast to some previous works on the subject which consider only single-particle disorders, disorders with general bounded spatial distributions are examined in this work. The impurity modes are asymptotically approximated using continuum approximation of the discrete chain and perturbation analysis. Numerical simulations verify the analytical predictions. The results of this study can be used to better understand the interaction between solitary waves and impurities in non-linear lattices.