2134/20751
Alexander Tovbis
Alexander
Tovbis
Gennady El
Gennady
El
Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach
Loughborough University
2016
Whitham equations
Semiclassical limit of the focusing NLS
Riemann-Hilbert Problem approach
Mathematical Sciences not elsewhere classified
2016-04-01 10:05:02
Journal contribution
https://repository.lboro.ac.uk/articles/journal_contribution/Semiclassical_limit_of_the_focusing_NLS_Whitham_equations_and_the_Riemann-Hilbert_Problem_approach/9386171
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.