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Semiclassical limit of the focusing NLS: Whitham equations and the Riemann–Hilbert Problem approach

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2016Embargo end date: 01 Jan 2016 United States Publisher:Elsevier BVJournal:Physica D: Nonlinear Phenomena, volume 333, pages 171-184 (issn: 0167-2789,

Authors: Tovbis, Alexander; El, Gennady A.;

doi: 10.1016/j.physd.2016.03.009 , 10.48550/arxiv.1603.03341

arXiv: http://arxiv.org/abs/1603.03341

Semiclassical limit of the focusing NLS: Whitham equations and the Riemann–Hilbert Problem approach

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Abstract

The main goal of this paper is to put together: a) the Whitham theory applicable to slowly modulated $N$-phase nonlinear wave solutions to the focusing nonlinear Schr��dinger (fNLS) equation, and b) the Riemann-Hilbert Problem approach to particular solutions of the fNLS in the semiclassical (small dispersion) limit that develop slowly modulated $N$-phase nonlinear wave in the process of evolution. Both approaches have their own merits and limitations. Understanding of the interrelations between them could prove beneficial for a broad range of problems involving the semiclassical fNLS.

28 pages, 2 figures

Country

United States

Related Organizations

Loughborough University
United Kingdom
Department of Mathematical Sciences Loughborough University
United Kingdom
University of Central Florida
United States
University of Central Florida
United States

Keywords

Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Semiclassical limit of the focusing NLS, Riemannâ€“Hilbert Problem approach, Exactly Solvable and Integrable Systems (nlin.SI), Whitham equations

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