On the Analyticity of the Spectral Density for Semiclassical NLS

Kamvissis, Spyridon (2012) On the Analyticity of the Spectral Density for Semiclassical NLS. (Unpublished)

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Abstract

In a previous work, we have analyzed the semiclassical behavior of solutions to the focusing,completely integrable nonlinear Schroedinger equation, under the assumption of real analytic initial data (among others). We have provided global semiclassical asymptotics under the so-called ”finite gap” assumption. In a subsequent paper, we have justified the ”finite gap” assumption, again under several assumptions, the main assumption being that the limiting spectral density of the eigenvalues of the associated Dirac operator has an analytic extension in the upper half-plane. In the present article, we show that this constraint is unnecessary. In fact, analyticity of the neccessary quantities in the analysis can be recovered via the solution of a scalar Riemann-Hilbert problem.

Item Type: Article
Depositing User: Professor Spyridon Kamvissis
Date Deposited: 11 Mar 2013 11:22
Last Modified: 21 Oct 2016 09:16
URI: http://preprints.acmac.uoc.gr/id/eprint/168

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