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arXiv · 1902.10622

On the radius of spatial analyticity for defocusing nonlinear Schr\"odinger equations

Jaeseop Ahn·Jimyeong Kim·Ihyeok Seo
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Abstract

In this paper we study spatial analyticity of solutions to the defocusing nonlinear Schr\"odinger equations $iu_t + \Delta u = |u|^{p-1}u$, given initial data which is analytic with fixed radius. It is shown that the uniform radius of spatial analyticity of solutions at later time $t$ cannot decay faster than $1/|t|$ as $|t|\rightarrow\infty$. This extends the previous work of Tesfahun for the cubic case $p=3$ to the cases where $p$ is any odd integer greater than $3$.

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Jaeseop Ahn, Jimyeong Kim, Ihyeok Seo. 2019-02-27. On the radius of spatial analyticity for defocusing nonlinear Schr\"odinger equations. https://arxiv.org/abs/1902.10622

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