%0 Journal Article %A Tovbis, Alexander %A El, Gennady %D 2016 %T Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach %U https://repository.lboro.ac.uk/articles/journal_contribution/Semiclassical_limit_of_the_focusing_NLS_Whitham_equations_and_the_Riemann-Hilbert_Problem_approach/9386171 %2 https://repository.lboro.ac.uk/ndownloader/files/16999367 %K Whitham equations %K Semiclassical limit of the focusing NLS %K Riemann-Hilbert Problem approach %K Mathematical Sciences not elsewhere classified %X 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. %I Loughborough University