  We present the theoretical background and detailed equations for the
synchrotron emission of a shock wave propagating in a relativistic jet. We then
show how the evolution of an outburst in this shock-in-jet scenario can be
analytically described and parameterized to be fitted to multi-frequency
lightcurves of galactic and extragalactic sources. This is done here for the
first time with a completely physical description of the jet and the shocked
gas, while previous studies used a more phenomenological approach based on the
observed properties of the outbursts. Another interesting addition to previous
work is the introduction of a low-energy cut of the electron energy
distribution that allows for much more diverse synchrotron spectral shapes. To
demonstrate and illustrate the new methodology, we present results of
infrared-to-radio lightcurve fitting of a succession of outbursts observed in
1994 in the microquasar Cyg X-3. We find that the diversity of outbursts in
shape, amplitude, frequency range and timescale can be fairly described by
varying only the strength of the shock and its build-up distance from the apex
of the jet. A rapid build-up results in high-frequency outbursts evolving on
short timescales, while slowly evolving, low-frequency outbursts form and
evolve further out in the jet. We conclude by outlining future developments, in
particular the inclusion of the associated synchrotron self-Compton emission at
X-rays and gamma-rays.
