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Loss of phase, universality of stochastic interactions, uncertainty quantification, and loss of reversibility

Banff International Research Station for Mathematical Innovation and Discovery

Previously, we showed that for all continuations of NLS blowup solutions, the phase is lost after the singularity. In this talk I will show that ``loss of phase'' can occur even if the NLS solution does not collapse. Therefore, if two NLS solutions travel a sufficiently long distance (time) before interacting, it is not possible to predict whether they would intersect in- or out-of-phase. Hence, a deterministic prediction of the interaction outcome becomes impossible. ``Fortunately'', because the relative phase between the two solutions becomes uniformly distributed in $[0,2\pi]$, the statistics of the interaction outcome is universal. The statistics can be efficiently computed using a novel Uncertainty-Quantification method, even when the distribution of the noise source is unknown. I will end by arguing that although the NLS has a time-reversal symmetry, its solutions can experience a loss of reversibility.

Mathematics; Partial differential equations; Fourier analysis

video/mp4

Author affiliation: Tel Aviv University

2019-12-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73012

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/