This chapter discusses the principle and application of two model‐based algorithms for processing non‐dispersive and dispersive ground penetrating radar (GPR) data over layered medium under monostatic antenna configuration. Both algorithms have been selected for their super‐time resolution capability and reduced computational burden; they allow GPR to measure a layer thickness smaller than the ...

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 ...

A fast, hybrid numerical–asymptotic algorithm for the calculation of the dynamical field evolution that is due to an arbitrary input pulse in any linear dispersive, attenuative medium is presented. The algorithm combines the numerical efficiency of the fast-Fourier-transform algorithm over a finite frequency domain that encompasses all the medium resonances with the accuracy and analytical effi...

Ž . We investigate the possibility of forming spatiotemporal solitons optical bullets in inhomogeneous, dispersive nonlinear media using a graded-index Kerr medium as an example. We use a variational approach to solve the multidimensional, inhomogeneous, nonlinear Schrodinger equation and show that spatiotemporal solitons can be stabilized under certain ̈ conditions. We verify their existence by...

While the non-homogeneous boundary value problem for elliptic, hyperbolic and parabolic equations is relatively well understood, there are still few results for general dispersive equations. We define here a convenient class of equations comprising the Schrödinger equation, the Airy equation and linear ‘Boussinesq type’ systems, which is in some sense a generalization of strictly hyperbolic equ...

We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system – which we show is essentially ...

We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system – which we show is essentially ...

The angular spectrum of plane waves representation of the freely propagating electromagnetic field in the halfspace z z of a homogeneous, isotropic, locally linear, temporally dispersive medium is employed to describe the polarization properties of the field throughout the half-space z > z in terms of the polarization behavior of either field vector on the plane at z = z. Both the spatial and t...

Using a dissipation-scale adaptive, wavelet-like shell decomposition method and normalization by dissipation-scale characteristics, we found a novel sustaining behavior of self-similarity in the quadratic energy transfer process in freely decaying, fully developed, homogeneous and isotropic turbulences of an incompressible Hall magnetohydrodynamic medium. The process is associated with the rela...

contains the elasticity modules of the medium. Usually one makes the assumption that S is positive definite such that A(D) is a positive and self-adjoint operator. Then the first equation is hyperbolic, while the second one is parabolic. In [2] the thermo-elastic system is considered and dispersive estimates are proven under the assumptions that (A1-2) A(ξ) is positive (self-adjoint, 2-homogene...