In recent years two nonlinear dispersive partial differential equations have attracted much attention due to their integrable structure. We prove that both equations arise in the modeling of the propagation of shallow water waves over a flat bed. The equations capture stronger nonlinear effects than the classical nonlinear dispersive Benjamin–Bona–Mahoney and Korteweg–de Vries equations. In par...

An approach to obtaining dispersive estimates for certain multidimensional linear hyperbolic systems will be described. The key result is a local energy decay estimate which provides the intermediate link between the generalized Sobolev inequality and the energy inequality. §

This paper introduces the concept of using the first subsymbol in the structure of a GFDM symbol as a pseudo circular preamble. Details about the motivation scenario in vehicular communication and the GFDM modulation are presented together with a prime estimation approach for isolating the preamble information from regular data. The concept aims to allow easy adaptation of state-of-the-art tech...

We study the dispersive properties of the wave equation associated with the shifted Laplace–Beltrami operator on real hyperbolic spaces and deduce new Strichartz estimates for a large family of admissible pairs. As an application, we obtain local well–posedness results for the nonlinear wave equation.

We prove dispersive estimates for solutions to the wave equation with a real-valued potential V ∈ L∞(R), n ≥ 4, satisfying V (x) = O(〈x〉−(n+1)/2−ǫ), ǫ > 0.

The authors present a review on the recent approaches proposed to implement transversal RF filters. Different tunable transversal filters consisting of wavelength tunable optical taps and those employing the tunability of dispersive devices are presented showing their high-performance characteristics. A comprehensive review of the fundamentals and a discussion on the main limitation of these st...

This talk describes the reasons why η and η decays are an interesting topic of study for both theory and experiment. The main part discusses the results of the recent calculation of η → 3π at two-loop order in ChPT. Some puzzling aspects of the results compared to earlier dispersive calculations are highlighted. I also like to remind the reader of the use of η and η decays for studying the anom...

The Casimir energy of a dilute homogeneous nonmagnetic dielectric ball at zero temperature is derived analytically within a microscopic realistic model of dielectrics for an arbitrary physically possible frequency dispersion of dielectric permittivity ε(iω). Divergences are absent in calculations, a minimum interatomic distance λ is a physical cut-off. Casimir surface force is proved to be attr...

The problems under consideration are related to wave propagation in nonlinear dispersive media, characterised by higher-order nonlinear and higher-order dispersive effects. Particularly two problems — wave propagation in dilatant granular materials and wave propagation in shape-memory alloys — are studied. Model equations are KdVlike evolution equations in both cases. The types of solutions are...