  We aim to identify the physical processes which occur in the magnetic network
of the chromosphere and which contribute to its dynamics and heating.
Specifically, we study the propagation of transverse (kink) MHD waves which are
impulsively excited in flux tubes through footpoint motions. When these waves
travel upwards, they get partially converted to longitudinal waves through
nonlinear effects (mode coupling). By solving the nonlinear, time-dependent MHD
equations we find that significant longitudinal wave generation occurs in the
photosphere typically for Mach numbers as low as 0.2 and that the onset of
shock formation occurs at heights of about 600 km above the photospheric base.
We also investigate the compressional heating due to longitudinal waves and the
efficiency of mode coupling for various values of the plasma $\beta$, that
parameterises the magnetic field strength in the network. We find that this
efficiency is maximum for field strengths corresponding to $\beta\approx 0.2$,
when the kink and tube wave speeds are almost identical. This can have
interesting observational implications. Furthermore, we find that even when the
two speeds are different, once shock formation occurs, the longitudinal and
transverse shocks exhibit strong mode coupling.
