  We employ the MultiConfiguraional Time-Dependent Hartree for Bosons (MCTDHB)
method to study excited states of interacting Bose-Einstein condensates
confined by harmonic and double-well trap potentials. Two approaches to access
excitations, a static and a dynamic one, have been studied and contrasted. In
static simulations the low-lying excitations have been computed by utilizing
the LR-MCTDHB method - a linear response theory constructed on-top of a static
MCTDHB solution. Complimentary, we propose two dynamic protocols that address
excitations by propagating the MCTDHB wave-function. In particular, we
investigate dipole-like oscillations induced by shifting the origin of the
confining potential and breathing-like excitations by quenching frequency of a
parabolic part of the trap. To contrast static predictions and dynamic results
we have computed time-evolutions and their Fourier transforms of several local
and non-local observables. Namely, we study evolution of the $\left< x(t)
\right>$, its variance $\operatorname{Var}(x(t))$, and of a local density
computed at a selected position. We found out that the variance is the most
sensitive and informative quantity - along with excitations it contains
information about the de-excitations even in a linear regime of the induced
dynamics. The dynamic protocols are found to access the many-body excitations
predicted by the static LR-MCTDHB approach.
