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arXiv · 1901.05934

Dispersive decay of small data solutions for the KdV equation

Mihaela Ifrim·Herbert Koch·Daniel Tataru
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Abstract

We consider the Korteweg-de Vries (KdV) equation, and prove that small localized data yields solutions which have dispersive decay on a quartic time-scale. This result is optimal, in view of the emergence of solitons at quartic time, as predicted by inverse scattering theory.

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Mihaela Ifrim, Herbert Koch, Daniel Tataru. 2019-01-17. Dispersive decay of small data solutions for the KdV equation. https://arxiv.org/abs/1901.05934

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