  The propagation of lower hybrid waves in the presence of ponderomotive
density fluctuations is considered. The problem is treated in two dimensions
and, in order to be able to correctly impose the boundary conditions, the waves
are allowed to evolve in time. The fields are described by i v_tau - \int v_xi
dzeta + v_{zeta zeta} + |v|^2 v = 0 where v is proportional to the electric
field, tau to time, and zeta and xi measure distances across and along the
lower hybrid ray. The behavior of the waves is investigated numerically. If the
amplitude of the waves is large enough, the spectrum of the waves broadens and
their parallel wavelength becomes shorter. The assumptions made in the
formulation preclude the application of these results to the lower hybrid
heating experiment on Alcator-A. Nevertheless, there are indications that the
physics embodied in this problem are responsible for some of the results of
that experiment.
