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arXiv · 2110.08372

Well-posedness and blowup for the dispersion-managed nonlinear Schr\"odinger equation

Jason Murphy·Tim Van Hoose
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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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Jason Murphy, Tim Van Hoose. 2021-10-15. Well-posedness and blowup for the dispersion-managed nonlinear Schr\"odinger equation. https://arxiv.org/abs/2110.08372

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