  Context. The youngest Galactic supernova remnant G1.9+0.3 is an interesting
target for next generation gamma-ray observatories. So far, the remnant is only
detected in the radio and the X-ray bands, but its young age of ~100 yrs and
inferred shock speed of ~14,000 km/s could make it an efficient particle
accelerator. Aims. We aim to model the observed radio and X-ray spectra
together with the morphology of the remnant. At the same time, we aim to
estimate the gamma-ray flux from the source and evaluated the prospects of its
detection with future gamma-ray experiments. Methods. We performed spherical
symmetric 1-D simulations with the RATPaC code, in which we simultaneously
solve the transport equation for cosmic rays, the transport equation for
magnetic turbulence, and the hydro-dynamical equations for the gas flow.
Separately computed distributions of the particles accelerated at the forward
and the reverse shock are then used to calculate the spectra of synchrotron,
inverse Compton, and pion-decay radiation from the source. Results. The
emission from G1.9+0.3 can be self-consistently explained within the
test-particle limit. We find that the X-ray flux is dominated by emission from
the forward shock while most of the radio emission originates near the reverse
shock, which makes G1.9+0.3 the first remnant with non-thermal radiation
detected from the reverse shock. The flux of very-high-energy gamma-ray
emission from G1.9+0.3 is expected to be close to the sensitivity threshold of
the Cherenkov Telescope Array, CTA. The limited time available to grow
large-scale turbulence limits the maximum energy of particles to values below
100 TeV, hence G1.9+0.3 is not a PeVatron.
