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math-ph2009★ 6 cited
Semiclassical limit of the scattering transform for the focusing Nonlinear Schr\" odinger Equation
Alexander Tovbis, Stephanos Venakides
The semiclassical limit of the focusing Nonlinear (cubic) Schr\" odinger Equation (NLS) corresponds to the singularly perturbed Zakharov Shabat (ZS) system that defines the direct…
math-ph2008★ 3 cited
Determinant form of modulation equations for the semiclassical focusing Nonlinear Schr\" odinger equation
Alexander Tovbis, Stephanos Venakides
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…