Semiclassical Limit Of The Focusing Nls: Whitham Equations And The Riemann–Hilbert Problem Approach

Keywords

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

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 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 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.

Publication Date

10-15-2016

Publication Title

Physica D: Nonlinear Phenomena

Volume

333

Number of Pages

171-184

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.physd.2016.03.009

Socpus ID

84964329941 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84964329941

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