Bragge Solitons in 1-d Diatomic Chain with Nonlinear Interatomic Interaction and Nonlinear on-Site Potential

Abstract

Soliton-like excitations with frequencies in the gap and near the gap of linear spectrum are considered for diatomic chain with small mass difference. The chains with the additional quartic anharmonic potential of nearest-neighbor interaction and quartic nonlinear interaction with external elastic substratum (on-site potential) are studied. It is shown that the localized excitations represent the complicated combination of solitons of acoustic and quasi-optical branches of the spectrum. Gap solitons are studied with the help of the methods of qualitative analysis of dynamical systems and of the method of asymptotical expansions. It is shown that when the frequency of soliton changes a number of bifurcations of the soliton solutions takes place. The bifurcation picture is different for different forms of nonlinearity in diatomic chain and depend on relation between nonlinear interaction constants. Solitons with the frequencies out of the gap have the form of bound state of “ bright'' and “ dark'' solitons or dark soliton and soliton on the pedestal.