  We numerically study the dynamics of Faraday waves in a pancake-shaped
Bose--Einstein condensate (BEC) subject to periodic modulation of the
interaction. After the modulation starts, Faraday waves appear and, thereafter,
the BEC enters the "nonlinear regime", in which several collective modes are
excited. By maintaining the modulation without dissipation, the kinetic energy
that contributes to the density gradient causes quasiperiodic motion and
increases monotonically. In the nonlinear regime, the dips in the density
similar to dark solitons move around in the BEC, intersecting with each other
and maintaining their shapes. On the other hand, even by turning off the
modulation, Faraday waves and the nonlinear regime appear. The kinetic energy
converges to the statistical steady state. The calculation of the modulation
with the dissipation illustrates the collapse and revival of Faraday waves.
When the dissipation is small, the appearance and collapse of the Faraday waves
and the nonlinear regime occur again.
