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Title: Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach
Authors: Tovbis, Alexander
El, G.A.
Keywords: Whitham equations
Semiclassical limit of the focusing NLS
Riemann-Hilbert Problem approach
Issue Date: 2016
Publisher: © Elsevier
Citation: TOVBIS, A. and EL, G., 2016. Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach. Physica D: Nonlinear Phenomena, DOI: 10.1016/j.physd.2016.03.009.
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 odinger (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 benefi cial for a broad range of problems involving the semiclassical fNLS.
Description: THIS DOCUMENT WILL REMAIN CLOSED ACCESS UNTIL 22/03/2017.
Sponsor: The work was supported in part by the Ban International Research Station, University of British Columbia, Vancouver, Canada. The work of the first author was supported in part by London Mathematical Society. The work of the second author was supported in part by the Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364.
Version: Accepted for publication
DOI: 10.1016/j.physd.2016.03.009
URI: https://dspace.lboro.ac.uk/2134/20751
Publisher Link: http://dx.doi.org/10.1016/j.physd.2016.03.009
ISSN: 0167-2789
Appears in Collections:Closed Access (Maths)

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