  We study analytically the dynamics of two-dimensional rectangular lattices
with periodic boundary conditions. We consider anisotropic initial data
supported on one low-frequency Fourier mode. We show that, in the continuous
approximation, the resonant normal form of the system is given by integrable
PDEs. We exploit the normal form result in order to prove the existence of
metastability phenomena for the lattices. More precisely, we show that the
energy spectrum of the normal modes attains a distribution in which the energy
is shared among a packet of low-frequencies modes; such distribution remains
unchanged up to the time-scale of validity of the continuous approximation.
