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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Whispering gallery waves diffraction by boundary inflection: an unsolved canonical problem

## Whispering gallery waves diffraction by boundary inflection: an unsolved canonical problemAdd to your list(s) Download to your calendar using vCal - Valery Smyshlyaev (University College London)
- Tuesday 13 August 2019, 16:30-17:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact INI IT. WHTW01 - Factorisation of matrix functions: New techniques and applications The problem of interest is that of a whispering gallery high-frequency asymptotic mode propagating along a concave part of a boundary and approaching a boundary inflection point. Like Airy ODE and associated Airy function are fundamental for describing transition from oscillatory to exponentially decaying asymptotic behaviors, the boundary inflection problem leads to an arguably equally fundamental canonical boundary-value problem for a special PDE , describing transition from a “modal” to a “scattered” high-frequency asymptotic behaviour. The latter problem was first formulated and analysed by M.M. Popov starting from 1970-s. The associated solutions have asymptotic behaviors of a modal type (hence with a discrete spectrum) at one end and of a scattering type (with a continuous spectrum) at the other end. Of central interest is to find the map connecting the above two asymptotic regimes. The problem however lacks separation of variables, except in the asymptotical sense at both of the above ends. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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