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Periodic traveling waves for nonlinear Schr\"odinger equations with non-zero conditions at infinity in $ \R ^2 $
We consider the nonlinear Schr\"odinger equation with nonzero conditions at infinity in $\R^2$. We investigate the existence of traveling waves that are periodic in the direction transverse to the direction of propagation and minimize the energy when the momentum is kept fixed. We show that for any given value of …