  The dynamical behavior of matter wave solitons of two-component Bose-Einstein
condensates (BEC) in combined linear and nonlinear optical lattices (OLs) is
investigated. In particular, the dependence of the frequency of the oscillating
dynamics resulting from initially slightly displaced components is investigated
both analytically, by means of a variational effective potential approach for
the reduced collective coordinate dynamics of the soliton, and numerically, by
direct integrations of the mean field equations of the BEC mixture. We show
that for small initial displacements binary solitons can be viewed as point
masses connected by elastic springs of strengths related to the amplitude of
the OL and to the intra and inter-species interactions. Analytical expressions
of symmetric and anti-symmetric mode frequencies, are derived and occurrence of
beatings phenomena in the displaced dynamics is predicted. These expressions
are shown to give a very good estimation of the oscillation frequencies for
different values of the intra-species interatomic scattering length, as
confirmed by direct numerical integrations of the mean field Gross-Pitaevskii
equations (GPE) of the mixture. The possibility to use displaced dynamics for
indirect measurements of BEC mixture characteristics such as number of atoms
and interatomic interactions is also suggested.
