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

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

2008-03-13

arxiv.org/abs/0803.2066v1

Physics

Mathematical Physics

11 pages, 2 figures, bibliography in a separate file

Scientific paper

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.

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