Long-time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space

摘要

The authors compute the long-time asymptotics for solutions of the NLSequation just under the assumption that the initial data lies in a weightedSobolev space. In earlier work (see e.g. [DZ1],[DIZ]) high orders of decay andsmoothness are required for the initial data. The method here is a furtherdevelopment of the steepest descent method of [DZ1], and replaces certainabsolute type estimates in [DZ1] with cancellation from oscillations.