Superluminal electromagnetic focus wave modes

A particular transformation of coordinates, associated with superluminal X-pulses, leaves the wave equation invariant and changes focus wave modes into superluminal focus wave pulses. Rather simple and manageable expressions for TM electromagnetic waves allow the investigation of these new localized solutions of Maxwell's equations. Received 11 June 2002 / Received in final form 27 August 2002 Published online 31 December 2002     

Symmetry groups and spiral wave solution of a wave propagation equation

We study a third-order nonlinear evolution equation, which can be transformed to the modified KdV equation, using the Lie symmetry method. The Lie point symmetries and the one-dimensional optimal system of the symmetry algebras are determined. Those symmetries are some types of nonlocal symmetries or hidden symmetries of the modified KdV equation. The group-invariant solutions, particularly the travelling wave and spiral wave solutions, are discussed in detail, and a type of spiral wave solution which is smooth in the origin is obtained.     

New Non-Travelling Wave Solutions of Calogero Equation

In this paper, the idea of a combination of variable separation approach and the extended homoclinic test approach is proposed to seek non-travelling wave solutions of Calogero equation. The equation is reduced to some (1+1)-dimensional nonlinear equations by applying the variable separation approach and solves reduced equations with the extended homoclinic test technique. Based on this idea and with the aid of symbolic computation, some new explicit solutions can be obtained.     

New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies

By a generalized bidirectional decomposition method, we obtain new Superluminal localized solutions to the wave equation (for the electromagnetic case, in particular) which are suitable for arbitrary frequency bands; several of them being endowed with finite total energy. We construct, among the others, an infinite family of generalizations of the so-called “X-shaped" waves. Results of this kind may find application in the other fields in which an essential role is played by a wave-equation (like acoustics, seismology, geophysics, gravitation, elementary particle physics, etc.). Received 23 June 2002 Published online 24 September 2002 RID="a" ID="a"Work partially supported by MIUR and INFN (Italy), and by FAPESP (Brazil). This paper did first appear as e-print physics/0109062 [and as preprint INFN/FM-01/02 (I.N.F.N.; Frascati, 2001)]. RID="b" ID="b"e-mail: recami@mi.infn.it     

High-Q whispering gallery modes in a spherical shell dielectric resonator: Characterization at microwave frequencies

We present a numerical and experimental characterization of high-Q whispering gallery resonant modes excited in a fused quartz spherical shell operated in the 18-26.5 GHz band; easy coupling and selection of modes is a most advantageous feature of the proposed structure with respect to ordinary bulk resonators. The numerical results, based on a finite element algorithm, well match experimental data, which also show the capability of our device to perform gaseous spectroscopy measurements. Received 25 October 2002 Published online 4 February 2003     

Attenuation of electromagnetic wave propagation in sandstorms incorporating charged sand particles

A theoretical approach for predicting the attenuation of microwave propagation in sandstorms is presented, with electric charges generated on the sand grains taken into account. It is found that the effect of electric charges distributed partially on the sand surface is notable. The calculated attenuation is in good agreement with that measured in certain conditions. The distribution of electric charges on the surface of sand grains, which is not easy to measure, can be approximately determined by measuring the attenuation value of electromagnetic waves. Some effects of sand radius, dielectric permittivity, frequency of electromagnetic wave, and visibility of sandstorms on the attenuation are also discussed quantitatively. Finally, a new electric parameter is introduced to describe the roles of scattering, absorption and effect of charges in attenuation.     

Complex Wave Excitations in Generalized Broer-Kaup System

Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function solutions） with arbitrary functions [or the （2＋ 1）-dimensional general/zed Broer-Kaup （GBK） system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the （2＋1）-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed.     

New Families of Rational Form Variable Separation Solutions to （2＋1）-Dimensional Dispersive Long Wave Equations

With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the （2＋1）-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.     

Mathieu Progressive Waves

A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal curvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.     

Variable Separation Approach to Solve (2 + 1)-Dimensional Generalized Burgers System:Solitary Wave and Jacobi Periodic Wave Excitations

By means of the standard truncated Painlev\'{e} expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakons, foldons, and previously revealed chaotic and fractal localized solutions, some new types of excitations --- compacton and Jacobi periodic wave solutions are obtained by introducing appropriate lower dimensional piecewise smooth functions and Jacobi elliptic functions.     

间歇性大气湍流中光传播问题的近Gauss极限分析

间歇性是湍流的重要特征，多年来一直是湍流研究的核心内容之一.考虑大气湍流中的光传播问题，一般回避其间歇性，假设大气介电起伏满足Gauss统计.考虑大气湍流（内）间歇性 对光波传播的影响.考虑到大气介电起伏方差较小的事实，将光场统计矩方程在Gauss场附近 展开到四阶累计量，分析其近似解.进一步，以层次结构模型为基础，着重研究了光场二阶 统计矩的间歇性效应.研究表明，大气湍流间歇性对光场的影响很小. 关键词： 光波传播 大气湍流 间歇性     

浅水体系中的多孤立波

形式分离变量法被推广应用于寻求不可积模型的多孤立波解.特别地,应用形式分离变量法于三个描述浅水体系的非线性方程:推广WhithamBroerKaup(WBK)方程、2+1维耦合KortewegdeVries(KdV)方程和1+1维耦合KdV方程,给出了这些体系的明显的解析的多孤立波解 关键词： 浅水体系 多孤立波 形式分离变量法 不可积模型     

非圆柱形发散梯度折射率棒透镜光线传播轨迹的解析解族

本文研究光线在具有非圆柱形等折射率面的发散型梯度折射率棒透镜中的传播规律,提出在轴向弱非匀条件(即dg~(-1)(z)/dz<<1下近轴子午光线轨迹的一种解析表达式.从该解析式的解析解,棒透镜梯度参数g(z)所满足的条件出发,导出棒透镜的折射率分布族.文中给出了两个线性无关的光线传播轨迹的解析解族,并以一种发散型棒透镜为例讨论了近轴成像特性.     

Numerical Approximation of Oscillatory Solutions of Hyperbolic-Elliptic Systems of Conservation Laws by Multiresolution Schemes

The generic structure of solutions of initial value problems of hyperbolic-elliptic systems, also called mixed systems, of conservation laws is not yet fully understood. One reason for the absence of a core well-posedness theory for these equations is the sensitivity of their solutions to the structure of a parabolic regularization when attempting to single out an admissible solution by the vanishing viscosity approach. There is, however, theoretical and numerical evidence for the appearance of solutions that exhibit persistent oscillations, so-called oscillatory waves, which are (in general, measure-valued) solutions that emerge from Riemann data or slightly perturbed constant data chosen from the interior of the elliptic region. To capture these solutions, usually a fine computational grid is required. In this work, a version of the multiresolution method applied to a WENO scheme for systems of conservation laws is proposed as a simulation tool for the efficient computation of solutions of oscillatory wave type. The hyperbolic-elliptic $2 \times 2$ systems of conservation laws considered are a prototype system for three-phase flow in porous media and a system modeling the separation of a heavy-buoyant bidisperse suspension. In the latter case, varying one scalar parameter produces elliptic regions of different shapes and numbers of points of tangency with the borders of the phase space, giving rise to different kinds of oscillation waves.     

A generic approach to boundary reflection in periodic media

Waves in periodic media, whose propagation is governed by nearest neighbour interaction, are investigated. The reflection and transmission coefficients are derived for a plane wave incident from medium 1 upon medium 2, without invoking common approximations. The derivation is valid for a class of waves including magneto- and electro-inductive waves, waves on short loaded dipoles, nanoparticles, coupled waveguides and acoustic waves in monatomic media. For this last case hitherto unknown microscopic reflection and transmission coefficients are derived and shown to reduce in the continuous limit to the well-known expressions in terms of acoustic impedances.     

(2+1)维非线性Burgers方程变量分离解和新型孤波结构

利用变量分离方法，获得了(2+1)维非线性Burgers方程的变量分离解.由于在Bcklund变换和变量分离步骤中引入了作为种子解的任意函数, 因而精确解中含有三个任意函数(其中一个为条件函数),适当地选择任意函数，可以获得多种形状的扭状孤波解、周期性孤子解和格子型孤波解. 关键词： 变量分离解 非线性波方程 （2+1）维     

(2+1)维色散长波方程的新精确解及其复合波激发

利用Riccati方程展开法和变量分离法,得到了(2+1)维色散长波方程的变量分离解.根据得到的孤波解,构造出该方程新颖的复合波局域结构,研究了复合波随时间的演化.