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We study the invisibility via anomalous localized resonance of a general source for electromagnetic waves in the setting of doubly complementary media. As a result, we show that cloaking is achieved if the power is blown up. We also reveal a critical length for the invisibility of a source that occurs when the plasmonic structure is complementary to an annulus of constant, isotropic medium.
A body of literature has developed concerning cloaking by anomalous localized resonance. The mathematical heart of the matter involves the behavior of a divergence-form elliptic equation in the plane, $ ablacdot (a(x) abla u(x)) = f(x)$. The complex-
This is a survey of approximate cloaking using transformation optics for acoustic and electromagnetic waves.
We prove the existence of infinitely many non square-integrable stationary solutions for a family of massless Dirac equations in 2D. They appear as effective equations in two dimensional honeycomb structures. We give a direct existence proof thanks t
We consider the nonlinear Klein-Gordon equation in $R^d$. We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the composing boosted
We consider dispersion generalized nonlinear Schrodinger equations (NLS) of the form $i partial_t u = P(D) u - |u|^{2 sigma} u$, where $P(D)$ denotes a (pseudo)-differential operator of arbitrary order. As a main result, we prove symmetry results for