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41 papers · 1 filter
Transparent scatterers and transmission eigenvalues
P. G. Grinevich, R. G. Novikov
{We give a short review of old and recent results on scatterers with transmission eigenvalues of infinite multiplicity, including transparent scatterers. Historically, these studie…
On non-uniqueness of phase retrieval in multidimensions
Roman Novikov, Tianli Xu
We give a large class of examples of non-uniqueness for the phase retrieval problem in multidimensions. Our constructions are based on "oblique tensorization", where one-dimensiona…
Phase recovery from phaseless scattering data for discrete Schrödinger operators
Roman Novikov, Basant Lal Sharma
We consider scattering for the discrete Schrödinger operator on the square lattice , , with compactly supported potential. We give formulas for finding the p…
Stabilization against collapse of 2D attractive Bose-Einstein condensates with repulsive, three-body interactions
Dinh-Thi Nguyen, Julien Ricaud
We consider a trapped Bose gas of identical bosons in two dimensional space with both an attractive, two-body, scaled interaction and a repulsive, three-body, scaled interactio…
On one-dimensional Bose gases with two- and (critical) attractive three-body interactions
Dinh-Thi Nguyen, Julien Ricaud
We consider a one-dimensional, trapped, focusing Bose gas where bosons interact with each other via both a two-body interaction potential of the form an…
Reconstruction of smooth shape defects in waveguides using locally resonant frequencies
Angèle Niclas, Laurent Seppecher
This article aims to present a new method to reconstruct slowly varying width defects in 2D waveguides using locally resonant frequencies. At these frequencies, locally resonant mo…