  We analyze the emergence of Shapiro resonances in tunnel-coupled
Bose-Einstein condensates, realizing a bosonic Josephson junction. Our analysis
is based on an experimentally relevant implementation using magnetic double
well potentials on an atomchip. In this configuration the potential bias
(implementing the junction voltage) and the potential barrier (realizing the
Josephson link) are intrinsically coupled. We show that the dynamically driven
system exhibits significantly enhanced Shapiro resonances which will facilitate
experimental observation. To describe the systems response to the dynamic drive
we compare a single-mode Gross-Pitaevskii (GP) description, an improved
two-mode (TM) model and the self-consistent multi-configurational time
dependent Hartree for Bosons (MCTDHB) method. We show that in the case of
significant atom-atom interactions or strong driving, the spatial dynamics of
the involved modes have to be taken into account, and only the MCTDHB method
allows reliable predictions.
