Modified scattering for the cubic Schr\"odinger equation small data solution on product space

Grace Liu

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arXiv · 1803.01921

Modified scattering for the cubic Schr\"odinger equation small data solution on product space

Grace Liu

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Abstract

In this paper we consider the long time behavior of solutions to the cubic nonlinear Schr\"odinger equation posed on the spatial domain $\mathbb{R}\times\mathbb{T}^{d}$, $1\leq d\leq4$. For sufficiently small, smooth, decaying data we prove global existence and derive modified asymptotic dynamics. We also consider the asymptotic completeness problem.

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Grace Liu. 2018-03-05. Modified scattering for the cubic Schr\"odinger equation small data solution on product space. https://arxiv.org/abs/1803.01921

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