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Uniform numerical-asymptotics for integrable systems via Riemann–Hilbert problems

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AR2W02 - Mathematics of beyond all-orders phenomena

Asymptotics for integrable systems such as the Korteweg–de Vries  and Painlevé equations can be proven rigorously using deformation of Riemann–Hilbert problems but this has traditionally only been used for special parameter regimes. In this talk we demonstrate that the Riemann–Hilbert problem also encodes uniform asymptotics, and that by incoporating numerics we can achieve asymptotically accurate computations of these equations. This also leads to the discovery of regions where the validity of current rigorous asymptotic expansions breaks down.

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

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