Loughborough University
Browse
NLS_RHP-PhysD_accepted.pdf (547.05 kB)

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

Download (547.05 kB)
journal contribution
posted 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.

Funding

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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Physica D: Nonlinear Phenomena

Volume

333

Pages

171-184

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, 333, pp. 171-184.

Publisher

© Elsevier

Version

  • AM (Accepted Manuscript)

Publisher statement

This 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/

Publication date

2016-03-21

Copyright date

2016

Notes

This 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.

ISSN

0167-2789

Language

  • en