NLS_RHP-PhysD_accepted.pdf (547.05 kB)
Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach
journal contributionposted on 2016-04-01, 10:05 authored by Alexander Tovbis, Gennady El
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.
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.
- Mathematical Sciences
Published inPhysica D: Nonlinear Phenomena
CitationTOVBIS, A. and EL, G., 2016. Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach. Physica D: Nonlinear Phenomena, 333, pp. 171-184.
- AM (Accepted Manuscript)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/
NotesThis paper was accepted for publication in the journal Physica D: Nonlinear Phenomena and the definitive published version is available at http://dx.doi.org/10.1016/j.physd.2016.03.009.