Consider the (cubic) nonlinear Schrodinger equation, with a generic potential, and small data. The case of zero potential is by now well understood (Ozawa, Kato-Pusateri), but the presence of a potential complicates matters since the Fourier transform cannot be used directly. Rather, one has to analyse the dynamics through the distorted Fourier transform adapted to the potential. This is joint work with F. Pusateri and F. Rousset.

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