  The dynamics of localized excitations in array of Bose-Einstein condensates
is investigated in the framework of the nonlinear lattice theory. The existence
of temporarily stable ground states displaying an atomic population
distributions localized on very few lattice sites (intrinsic localized modes),
as well as, of atomic population distributions involving many lattice sites
(envelope solitons), is studied both numerically and analytically. The origin
and properties of these modes are shown to be inherently connected with the
interplay between macroscopic quantum tunnelling and nonlinearity induced
self-trapping of atoms in coupled BECs. The phenomenon of Bloch oscillations of
these excitations is studied both for zero and non zero backgrounds. We find
that in a definite range of parameters, homogeneous distributions can become
modulationally unstable. We also show that bright solitons and excitations of
shock wave type can exist in BEC arrays even in the case of positive scattering
length. Finally, we argue that BEC array with negative scattering length in
presence of linear potentials can display collapse.
