Alexei Rybkin: The Cauchy problem for the Korteweg-de Vries equation beyond standard assumption on initial data

Abstract:

We show that the Cauchy problem for the KdV equation can be solved by the inverse scattering transform (IST) for any initial data essentially bounded from 

below, decaying sufficiently rapidly at plus infinity, but unrestricted otherwise. Thus no pattern of behavior is required at minus infinity.

Our approach relies on new technics based on Hankel operators. Main results are complete.