The modulational instability and collapse of waves in the vicinity of
the lower-hybrid resonance including both magnetosonic and lower-hybri
d waves are investigated by analytical and numerical methods. The mech
anism leading to the modulational instability is the nonlinear couplin
g of lower-hybrid waves with the much lower-frequency quasineutral den
sity perturbations via the ponderomotive force. The result is a filame
ntation of the high-frequency field producing elongated, cigar-shaped
nonlinear wave packets aligned along the magnetic field with the plasm
a expelled outside (cavities). The analytical self-similar solutions d
escribing cavity collapse are obtained and compared with the results o
f numerical simulation for both two-and three-dimensional cavity geome
tries. It is shown that in three-dimensional solutions the transverse,
with respect to the magnetic field, contraction remains prevailing. T
he possibility of ion acceleration as the result of the lower-hybrid c
ollapse is discussed and detailed comparison is made with the observat
ions of the phenomena in the auroral ionosphere.