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

P. Deift·X. Zhou
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Abstract

The authors compute the long-time asymptotics for solutions of the NLS equation just under the assumption that the initial data lies in a weighted Sobolev space. In earlier work (see e.g. [DZ1],[DIZ]) high orders of decay and smoothness are required for the initial data. The method here is a further development of the steepest descent method of [DZ1], and replaces certain absolute type estimates in [DZ1] with cancellation from oscillations.

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P. Deift, X. Zhou. 2002-06-23. Long-time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space. https://arxiv.org/abs/math/0206222

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