The Phenomenon of Dispersive Revivals
Duration: 59 mins 44 secs
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| Description: |
Beatrice Pelloni Heriot-Watt University
15 June 2021 – 13:30 to 14:30 |
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| Created: | 2021-06-16 11:52 |
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| Collection: | Applicable resurgent asymptotics: towards a universal theory |
| Publisher: | Isaac Newton Institute for Mathematical Sciences |
| Copyright: | Beatrice Pelloni |
| Language: | eng (English) |
| Abstract: | I will give an overview of known and new results on the phenomenon of “dispersive quantisation” or “revivals”. A manifestation of this phenomenon is the re-emergence of an initial discontinuous pattern in the solution of periodic problems, at infinitely many points in time. Although 3 first reported in 1835 by Talbot, this phenomenon was only studied in the 90’s, in particular for the periodic free space Schroedinger equation by Berry and al . It was then rediscovered for the Airy equation by Peter Olver in 2010. Since then, a sizeable literature has examined revivals for the periodic problem for linear dispersive equations with polynomial dispersion relation. What I will discuss in this talk is further occurrences of this phenomenon for different boundary conditions, a novel form of revivals for more general dispersion relations and nonlocal equations such as the linearised BenjaminOno equation, and nonlinear (integrable) generalisations. This work is in collaboration with Lyonell Boulton, George Farmakis, Peter Olver and David Smith. |
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