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Boundary value problems on a finite interval, fractalisation and revivals

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CATW01 - The complex analysis toolbox: new techniques and perspectives

I will describe the behaviour of equations posed on a finite interval, and in particular the “Talbot effect”, a phenomenon known in optics and quantum mechanics, studied by M. Berry in the 1990s and re-discovered in the context of dispersive equations by Peter Olver in recent years. In this context, this
effect implies that the solution of periodic problems exhibits either revivals of the initial condition, or fractalisation. To study the extent of this effect, we use the solution representation obtained by the Unified Transform of Fokas, and numerical experimentation. This is joint work with David Smith, Lyonell Boulton and George Farmakis.

This talk is part of the Isaac Newton Institute Seminar Series series.

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