2–6 sept. 2019
Institut de Mathématiques de Bourgogne
Fuseau horaire Europe/Paris

Inverse Scattering for the Intermediate Long Wave Equation

5 sept. 2019, 09:00
45m
Amphi Paris

Amphi Paris

Orateur

Peter Perry (University of Kentucky)

Description

This talk reports on joint work with Joel Klipfel (University of Kentucky) and Yilun Wu (University of Oklahoma). The intermediate long wave equation (ILW) is a model of weakly nonlinear wave propagation in a fluid of finite depth. It interpolates between the Benjamin-Ono equation (infinite depth) and the Korteweg-de Vries equation (shallow water). Ablowitz and Kodama showed that ILW is completely integrable and, subsequently, an inverse scattering approach to solving ILW was developed by Ablowitz-Kodama-Satsuma and Santini-Ablowitz-Fokas. Our work is, to our knowledge, the first rigorous analysis of direct and inverse scattering maps for ILW. Both the direct and inverse problems are Riemann-Hilbert problems (respectively local and non-local); their proper formulation involves several interesting technical challenges.

Auteur principal

Peter Perry (University of Kentucky)

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