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

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Tovbis, A; Venakides, S

Published Date

  • 2009