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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
14/2005

Semiclassical Limit of the Focusing Nonlinear Schrödinger Equation under Barrier Initial Data

Spyridon Kamvissis

Abstract

We study the semiclassical behavior of the focusing nonlinear Schrödinger equation in 1+1 dimensions under discontinuous "barrier" initial data and we describe the violent oscillations arising in terms of theta functions. The construction of proofs relies on the analysis of the associated Riemann-Hilbert factorization problem.

Received:
Feb 20, 2005
Published:
Feb 20, 2005
Keywords:
semiclassical, nonlinear schrödinger equation, riemann-hilbert problems

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Preprint
2005 Repository Open Access
Spyridon Kamvissis

Semiclassical limit of the focusing nonlinear Schrödinger equation under barrier initial data