  It is shown how to compute the instability rates for the double-periodic
solutions to the cubic NLS (nonlinear Schrodinger) equation by using the Lax
linear equations. The wave function modulus of the double-periodic solutions is
periodic both in space and time coordinates; such solutions generalize the
standing waves which have the time-independent and space-periodic wave function
modulus. Similar to other waves in the NLS equation, the double-periodic
solutions are spectrally unstable and this instability is related to the bands
of the Lax spectrum outside the imaginary axis. A simple numerical method is
used to compute the unstable spectrum and to compare the instability rates of
the double-periodic solutions with those of the standing periodic waves.
