5 citations · 8 across the 9 of their papers we have counts for
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The DC Kerr Effect in Nonlinear Optics
Nikolas Eptaminitakis, Plamen Stefanov
We use weakly nonlinear geometric optics to study a model for the DC Kerr effect (the Kerr electro-optic effect), in which a light beam propagating through a material with strong n…
The hyperbolic X-ray transform: new range characterizations, mapping properties and functional relations
Nikolas Eptaminitakis, François Monard, Yuzhou Zou
We derive new singular value decompositions and range characterizations for the X-ray transform on the Poincaré disk, intertwining relations with distinguished differential operato…
Weakly nonlinear geometric optics for the Westervelt equation and recovery of the nonlinearity
Nikolas Eptaminitakis, Plamen Stefanov
We study the non-diffusive Westervelt equation in the weakly nonlinear regime. We show that the leading profile equation is of Burgers' type. We show that a compactly supported non…
The solid-fluid transmission problem
Nikolas Eptaminitakis, Plamen Stefanov
We study microlocally the transmission problem at the interface between an isotropic linear elastic solid and a linear inviscid fluid. We set up a system of evolution equations des…
Stability Estimates for the X-Ray Transform on Simple Asymptotically Hyperbolic Manifolds
Nikolas Eptaminitakis
We study the normal operator to the geodesic X-ray transform on functions in the setting of simple asymptotically hyperbolic manifolds. We construct a parametrix for the normal ope…