Determinant form of modulation equations for the semiclassical focusing Nonlinear Schr\" odinger equation

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We derive a determinant formula for the WKB exponential of singularly perturbed Zakharov-Shabat system that corresponds to the semiclassical (zero dispersion) limit of the focusing Nonlinear Schr\" odinger equation. The derivation is based on the Riemann-Hilbert Problem (RHP) representation of the WKB exponential. We also prove its independence of the branchpoints of the corresponding hyperelliptic surface assuming that the modulation equations are satisfied.
11 pages, 2 figures, bibliography in a separate file

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Mathematical Physics, Analysis of PDEs

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http://salesiana.dossiersoluciones.com/handle/123456789/156888

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0803.2066
 http://arxiv.org/abs/0803.2066

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arXiv