WELL-POSEDNESS AND BLOWUP FOR THE DISPERSION-MANAGED NONLINEAR SCHRÖDINGER EQUATION
We consider the nonlinear Schrödinger 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.
J. Murphy and T. V. Hoose, "WELL-POSEDNESS AND BLOWUP FOR THE DISPERSION-MANAGED NONLINEAR SCHRÖDINGER EQUATION," Proceedings of the American Mathematical Society, vol. 151, no. 6, pp. 2489 - 2502, American Mathematical Society, Jun 2023.
The definitive version is available at https://doi.org/10.1090/proc/16243
Mathematics and Statistics
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01 Jun 2023