Alexei Rybkin (University of Alaska, Fairbanks)

Hankel operators and the Cauchy problem for the Korteweg-de Vries equation

Abstract:

In the context of the Cauchy problem for the Korteweg - de Vries equation, we show that the classical inverse scattering transform (IST) can be conveniently formulated in terms of the Hankel operator that allows us to apply some deep results from its theory to integrable PDEs. In particular, we show that this way we can extend the IST far beyond classical initial data.