Semi-classical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert problem approach

Gennady El, Alex Tovbis

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)171 -184
JournalPhysica D: Nonlinear Phenomena
Volume333
Early online date21 Mar 2016
DOIs
Publication statusPublished - 15 Oct 2016

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