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.