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arXiv · 1603.03341

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

Alexander Tovbis·Gennady A. El
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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 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 beneficial for a broad range of problems involving the semiclassical fNLS.

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Alexander Tovbis, Gennady A. El. 2016-03-10. Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach. https://doi.org/10.1016/j.physd.2016.03.009

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