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Description: |
The Korteweg-de Vries equation (KdV), derived in the late 1800's to describe shallow-water waves, is one of the simplest but most fundamental examples of a partial differential equation combining nonlinear and dispersive effects. In constructing solutions, we often assume that particular structures of the initial data (say boundedness, periodicity, decay) are retained by the solution at a later time. In 2008, P. Deift conjectured that this should be true for solutions to KdV arising from almost periodic initial data (i.e., functions which are arbitrarily close to being periodic).
We will show that this is not always the case, with the enemy to almost periodicity coming from an unexpected origin: the dispersion, not the nonlinearity! We will see how the loss of almost periodicity is linked with an interesting optical experiment of Talbot in 1836, and how the completely integrable nature of KdV plays an important role in understanding these exotic solutions.
This talk is based on joint work with Rowan Killip and Monica Visan.
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Date: |
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| Start Time: |
15:00 |
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Speaker: |
Andreia Chapouto (University of Edinburgh, UK)
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Institution: |
School of Mathematics, University of Edinburgh, UK
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Place: |
Room 5.4 and remotely
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| Research Groups: |
-Analysis
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See more:
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