At the core of this article is an improved, sharp dispersive estimate for the anisotropic linear semigroup e1 arising in both the study of the dispersive SQG equation and the inviscid Boussinesq system. We combine the decay estimate with a blow-up criterion to show how dispersion leads to long-time existence of solutions to the dispersive SQG equation, improving the results obtained using hyper...

In the vast literature on tsunami research, few articles have been devoted to energy issues. A theoretical investigation on the energy of waves generated by bottom motion is performed here. We start with the full incompressible Euler equations in the presence of a free surface and derive both dispersive and non-dispersive shallowwater equations with an energy equation. It is shown that dispersi...

Internal erosional behaviour of lignosulfonate treated dispersive clay has been studied using the Process Simulation Apparatus for Internol Crack Erosion (PSAICE) designed and built at UOw. Effectiveness of Iignosulfonate treated dispersive clay on the erosion resistance has been investigated and its advantage over traditional admixtures is presented. Test results show that the hydraulic shear ...

Nowadays, dispersive mirrors are able to cover the wavelength range of 4.5 optical octaves and can be used from 220 nm up to 4500 nm. Various design approaches to dispersive mirrors in visible and near IR are briefly discussed. We consider in more detail two dispersive mirrors representing extreme cases. The first one is a mirror working in the range of 290−360 nm and providing group delay dis...

This paper presents a comprehensive analytical study of temporal modulation instabilities in a finite, nonlinear, dispersive medium in which two counterpropagating pump beams interact through a Kerr-type nonlinearity. The analysis includes selfand cross-phase modulations, group-velocity dispersion, four-wave mixing, and reflections occurring at the two facets of the dispersive Kerr medium. The ...

Sporadic-E (Es) is a layer of ionization that irregularly appears within the E region of the ionosphere and is known to generate an unusual propagation of very high frequency waves over long distances. The detailed spatial structure of Es remains unclear due to the limited spatial resolution in the conventional ionosonde observations. We detect midlatitude Es by interferometric synthetic apertu...

This presentation discusses different Zakharenko waves (ZWs) such as the non-dispersive ZWs, dispersive leaky ZWs, slow surface ZWs and ultrasonic surface ZWs, as well as their possible applications. The nondispersive Zakharenko waves can be found in complex systems such as different layered and quantum systems. Existence examples of the non-dispersive Zakharenko waves in both fundamental modes...

In order to obtain a unified approach for the FiniteDifference Time-Domain (FDTD) analysis of dispersive media described by a variety of models, the coordinate stretched Maxwell’s curl equation in time domain is firstly deduced. Then the FDTD update formulas combined with the semi-analytical recursive convolution (SARC) in Digital Signal Process (DSP) technique for general dispersive media are ...

The paper describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on the global canonical transforms and the underlying global microlocal analysis. For this purpose, the Egorov-type theorem is established with canonical transformations in the form of a class of Fourier integral operators, and their weighted L–boundedness properties are d...