  We calculate magnon lifetime in an easy-plane ferromagnet on a tetragonal
lattice in transverse magnetic field. At zero temperature magnons are unstable
with respect to spontaneous decay into two other magnons. Varying ratio of
intrachain to interchain exchanges in this model we consider the effect of
dimensionality on spontaneous magnon decay. The strongest magnon damping is
found in the quasi-one-dimensional case for momenta near the Brillouin zone
boundary. The sign of a weak interchain coupling has a little effect on the
magnon decay rate. The obtained theoretical results suggest possibility of
experimental observation of spontaneous magnon decay in a quasi-one-dimensional
ferromagnet CsNiF$_3$. We also find an interesting enhancement of the magnon
decay rate for a three-dimensional ferromagnet. The effect is present only for
the nearest-neighbor model and is related to effective dimensionality reduction
in the two-magnon continuum.
