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Schrödinger equations with nonlinearity of integral type
We consider the Cauchy problem for the nonlinear Schrödinger
equation with interaction described by the integral
of the intensity with respect to one direction in two space dimensions.
Concerning the problem with finite initial time, we prove
the global well-posedness in the largest space $L^2(\mathbb R^2)$. Concerning
the problem with infinite initial time, we prove the existence of modified
wave operators on a dense set of small and
sufficiently regular asymptotic states.