We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized state, and also reveal a generic physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances.

silicon thin layers are deposited on glass substrates with the thickness of 103 nm, 147 nm and 197 nm. the layers are produced with electron gun evaporation method under ultra-high vacuum condition. the optical reectance and the transmittance of produced layers were measured by using spectrophotometer. the optical functions such as, real and imaginary part of refractive index, real and imaginar...

The Kramers-Kronig relations are derived for the permittivity of the usual plasma model which neglects dissipation and of a generalized model which takes into account the interband transitions. The generalized plasma model is shown to be consistent with all precision experiments on the measurement of the Casimir force.

Our current understanding of the absorption and emission properties of interstellar grains are reviewed. The constraints placed by the Kramers-Kronig relation on the wavelength-dependence and the maximum allowable quantity of the dust absorption are discussed. Comparisons of the opacities (mass absorption coefficients) derived from interstellar dust models with those directly estimated from obs...

A simple Kronig-Penney model is used to study the effect of nonlinear interactions on the electronic properties of ordered and disordered electrified chains. In the case of ordered potentials, we found that the nonlinearity suppresses the Wannier-Stark effect caused by the electric field. In the case of disordered potentials, the nonlinearity gives rise to a transition from superlocalized to we...

The known correspondence between the Kronig{Penney model and certain Jacobi matrices is extended to a wide class of Schrr odinger operators on graphs. Examples include rectangular lattices with and without a magnetic eld, or comb{ shaped graphs leading to a Maryland{type model.