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

Instability of double-periodic waves in the nonlinear Schrodinger equation