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Monday, February 14, 2005

**Abstract:** Abstract: We consider the (linearized) stability of a standing wave solution to the nonlinear Schrodinger equation with a periodic potential. We give a general condition (non-perturbative) which guarantees the existence of a modulational instability. In the case of weak nonlinearity this instability has a nice interpretation in terms of the "effective mass" of a particle in the periodic potential. This is joint work with Zoi Rapti.