Modified Scattering for Nonlocal Nonlinear Schr\"odinger Equations

Tim Van Hoose

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arXiv · 2511.06637

Modified Scattering for Nonlocal Nonlinear Schr\"odinger Equations

Tim Van Hoose

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Abstract

We prove a modified scattering and sharp $L^\infty$ decay result for both the Hartree and Schr\"odinger-Bopp-Podolsky equations in dimensions $2$ and $3$ using the testing by wavepackets approach due to Ifrim and Tataru. We show that modified scattering and sharp pointwise decay occur for these equations at a regularity much lower than previous results due to Hayashi-Naumkin and Kato-Pusateri, and as a corollary also show that the results on power-type scattering-critical NLS due to Hayashi-Naumkin can be proven under minimal regularity assumptions.

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Tim Van Hoose. 2025-11-10. Modified Scattering for Nonlocal Nonlinear Schr\"odinger Equations. https://arxiv.org/abs/2511.06637

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