  We describe and rigorously justify the nonlinear interaction of highly
oscillatory waves in nonlinear Schrodinger equations, posed on Euclidean space
or on the torus. Our scaling corresponds to a weakly nonlinear regime where the
nonlinearity affects the leading order amplitude of the solution, but does not
alter the rapid oscillations. We consider initial states which are
superpositions of slowly modulated plane waves, and use the framework of Wiener
algebras. A detailed analysis of the corresponding nonlinear wave mixing
phenomena is given, including a geometric interpretation on the resonance
structure for cubic nonlinearities. As an application, we recover and extend
some instability results for the nonlinear Schrodinger equation on the torus in
negative order Sobolev spaces.
