22 citations · 112 across the 18 of their papers we have counts for
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An Exactly Solvable Model for Nonlinear Resonant Scattering
Stephen P. Shipman, Stephanos Venakides
This work analyzes the effects of cubic nonlinearities on certain resonant scattering anomalies associated with the dissolution of an embedded eigenvalue of a linear scattering sys…
Perturbation of Riemann-Hilbert jump contours: smooth parametric dependence with application to semiclassical focusing NLS
Sergey Belov, Stephanos Venakides
A perturbation of a class of scalar Riemann-Hilbert problems (RHPs) with the jump contour as a finite union of oriented simple arcs in the complex plane and the jump function with…
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…
Nonlinear steepest descent asymptotics for semiclassical limit of integrable systems: Continuation in the parameter space
Alexander Tovbis, Stephanos Venakides
The initial value problem of an integrable system, such as the Nonlinear Schr\" odinger equation, is solved by subjecting the linear eigenvalue problem arising from its Lax pair to…
Fano-Type Resonance of Waves in Periodic Slabs
Natalia Ptitsyna, Stephen P. Shipman, Stephanos Venakides
We investigate Fano-type anomalous transmission of energy of plane waves across lossless slab scatterers with periodic structure in the presence of non-robust guided modes. Our app…
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…