Geometrical theory of diffraction for high‐frequency coherence functions in a weakly random medium with inhomogeneous background profile

Geometrical theory of diffraction.

A Weakly Nonlinear Alfvénic Pulse in a Transversely Inhomogeneous Medium

The interaction of a weakly nonlinear Alfvénic pulse with an Alfvén speed inhomogeneity in the direction perpendicular to the magnetic field is investigated. Identically to the phase mixing experienced by a harmonic Alfvén wave, sharp transverse gradients are generated in the pulse by the inhomogeneity. In the initial stage of the evolution of an initially plane Alfvénic pulse, the transverse g...

Stokes-vector evolution in a weakly anisotropic inhomogeneous medium.

The equation for evolution of the four-component Stokes vector in weakly anisotropic and smoothly inhomogeneous media is derived on the basis of a quasi-isotropic approximation of the geometrical optics method, which provides the consequent asymptotic solution of Maxwell's equations. Our equation generalizes previous results obtained for the normal propagation of electromagnetic waves in strati...

Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach.

We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the desc...

Random coincidence point results for weakly increasing functions in partially ordered metric spaces

The aim of this paper is to establish random coincidence point results for weakly increasing random operators in the setting of ordered metric spaces by using generalized altering distance functions. Our results present random versions and extensions of some well-known results in the current literature.