Determinant form of modulation equations for the semiclassical focusing Nonlinear Schr\" odinger equation
arXiv:0803.2066
Abstract
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