2-6 September 2019
Institut de Mathématiques de Bourgogne
Europe/Paris timezone

Inverse Scattering for the Intermediate Long Wave Equation

5 Sep 2019, 09:00
45m
Amphi Paris ()

Amphi Paris

Speaker

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.

Primary author

Peter Perry (University of Kentucky)

Presentation Materials