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

Tovbis, Alexander and El, Gennady (2016) Semiclassical limit of the focusing NLS: Whitham equations and the Riemann–Hilbert Problem approach. Physica D: Nonlinear Phenomena, 333. pp. 171-184. ISSN 0167-2789

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Abstract

The main goal of this paper is to put together: a) the Whitham theory applicable to slowly modulated -phase nonlinear wave solutions to the focusing nonlinear Schrödinger (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 -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.

Item Type:	Article
Uncontrolled Keywords:	Semiclassical limit of the focusing NLS, Whitham equations, Riemann–Hilbert Problem approach
Subjects:	F300 Physics
Department:	Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User:	Becky Skoyles
Date Deposited:	03 Dec 2018 15:45
Last Modified:	11 Oct 2019 18:17
URI:	http://nrl.northumbria.ac.uk/id/eprint/37050

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