Dispersive decay of small data solutions for the KdV equation

Published 17 Jan 2019 in math.AP | (1901.05934v2)

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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