  Following a `bottom-up approach' in understanding many-particle effects and
dynamics we provide a systematic ab initio study of the dependence of the
breathing dynamics of ultracold bosons in a 1D harmonic trap on the number of
bosons ranging from few to many. To this end, we employ the Multi-Layer
Multi-Configuration Time-Dependent Hartree method for Bosons (ML-MCTDHB) which
has been developed very recently [S. Kr\"onke, L. Cao, O. Vendrell and P.
Schmelcher. {\it New J. Phys.} {\bf 15}, 063018 (2013)]. The beating behavior
for two bosons is found numerically and consequently explained by an analytical
approach. Drawing on this, we show how to compute the complete breathing mode
spectrum in this case. We examine how the two-mode breathing behavior of two
bosons evolves to the single-frequency behavior of the many-particle limit when
adding more particles. In the limit of many particles, we numerically study the
dependence of the breathing mode frequency on both the interaction strength as
well as on the particle number. We provide an estimate for the parameter region
in which Gross-Pitaevskii theory is well applicable.
