Well-posedness and blowup for the dispersion-managed nonlinear Schr\"odinger equation
Abstract
We consider the nonlinear Schr\"odinger equation with periodic dispersion management. We first establish global-in-time Strichartz estimates for the underlying linear equation with suitable dispersion maps. As an application, we establish a small-data scattering result for the 3d cubic equation. Finally, we use a virial argument to demonstrate the existence of blowup solutions for the 3d cubic equation with piecewise constant dispersion map.
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