43 citations · 378 across the 28 of their papers we have counts for
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math-ph2014★ 4 cited
Oscillatory and localized perturbations of periodic structures and the bifurcation of defect modes
Vincent Duchêne, Iva Vukićević, Michael I. Weinstein
Let denote a periodic function on the real line. The Schrödinger operator, , has spectrum equal to the union of closed real interv…
math-ph2013★ 15 cited
Homogenized description of defect modes in periodic structures with localized defects
Vincent Duchêne, Iva Vukićević, Michael I. Weinstein
A spatially localized initial condition for an energy-conserving wave equation with periodic coefficients disperses (spatially spreads) and decays in amplitude as time advances. Th…
math-ph2010★ 16 cited
Scattering, homogenization and interface effects for oscillatory potentials with strong singularities
Vincent Duchêne, Michael I. Weinstein
We study one-dimensional scattering for a decaying potential with rapid periodic oscillations and strong localized singularities. In particular, we consider the Schrödinger equatio…