Anomalous behaviour in a Bragg reflection waveguide

A novel asymmetric Bragg reflection waveguide (BRW) showing anomalous dispersion characteristic is presented. The abnormal behaviour of increase of modal effective index with wavelength is primarily caused by the changes taking place in the imaginary part of the Bloch wavevector, in the periodic stratified cladding. The phase velocity and the group velocity dispersion characteristics for the waveguide have also been analyzed. Such an anomalous behaviour can find applications in the design of integrated optical devices.     

Stationary waves described by a generalized KdV-burgers equation

We have obtained solutions in the form of stationary waves within the framework of the generalized KdV-Burgers equation, which contains nonconservative terms of linear pump, linear HF dissipation, and nonlinear dissipation. Both periodic and solitary waves are analyzed. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 10, pp. 1241–1248, October, 1997.     

Anomalous microwave reflection from a metal surface induced by spoof surface plasmon

The reflection of X-band microwaves (8-12 GHz) from a metallic aluminum (Al) surface with groove grating corrugations was investigated experimentally. It was shown that the reflection of p-polarization is much less than the microwave reflected from the corresponding area of an unruled Al surface, with selective wavelength. The experimental results demonstrated that the anomalous microwave reflection is strongly associated with the excitation of spoof surface plasmons at the Al-air interface by the surface grating coupler. This near-total absence of reflected microwaves is similar to the famous Wood's anomaly in the optical regime and is of fundamental importance to the applications of spoof surface plasmons in the microwave regime.     

Random integral equation formulation of a generalized Langevin equation

In this paper, the generalized Langevin equation introduced by Kubo and Mori is formulated as a random integral equation. We consider (1) the existence and uniqueness of the solution, (2) moments of the solution process, (3) a comparison theorem for solution processes, and (4) the Cauchy polygonal approximation to the solution.     

Anomalous diffusion in generalized Dykhne model

Contaminant transport is investigated in the generalized Dykhne model differing from the original Dykhne model by the presence of advection in the high-permeability medium. An analysis is presented of transport regimes and concentration tail behavior in the high-permeability medium. It is found that the transport regimes include anomalous ones: subdiffusion and quasi-diffusion. A difference is revealed between longitudinal and transverse transport. Regime change over time leads to multiple-regime long-distance asymptotic behavior of concentration distributions. An analogy is drawn between the problems examined here and transport through comb structures.     

Heat Fluctuations and a generalized Gibbs equation

Starting from a generalized Gibbs equation and from the Einstein formula for the probability of fluctuations, we obtain the correlation function of heat fluctuations.     

Charmonium spectrum with a generalized Fermi-Breit equation

A recently derived Fermi-Breit equation for a non-Coulombic vector interaction is used to construct a specific model for the charmonium spectrum. A scalar interaction term is also considered. Momentum-dependent terms, generated by the requirement of relativistic covariance, are included in the model.     

On the equivalence of generalized Langevin equation and generalized master equation

It is shown that the generalized Langevin equation derived by Mori is equivalent to the generalized master equation of Nakajima and Zwanzig. Both equations of motion are related, just in the same way as Heisenberg and Schrödinger picture are related.     

反常扩散与分数阶对流-扩散方程

反常扩散现象在自然界和社会系统中广泛存在.考虑了扩散过程的时间相关和时空相关性，用非局域性的处理方法，在传统的二阶对流 扩散方程基础上，得到了分数阶对流 扩散方程，以此方程来描述反常扩散.在此方程中，弥散项和对时间的导数为分数阶导数所代替.由此分数阶对流 扩散方程，对传统的费克扩散定律进行推广，得到了广义的分数费克扩散定律，分数费克扩散定律说明某时刻空间中某点的流量不仅与其领域内的浓度梯度有关，而且与整个空间中其他不同点的粒子浓度、浓度变化的历史，甚至初始时刻的浓度有关.讨论了方程的解——分数稳定分布，并由此说明了扩散运动的平均平方位移是运移时间的非线性函数. 关键词： 扩散 分数阶微积分 稳定分布（Lévy分布） 费克扩散定律     

Anomalous reflection of light in novel distributed-feedback structures

The possibility that lasing can occur in a rippled waveguide structure containing a high-reflectivity layer is studied. Lasing is achieved experimentally in a waveguide structure with an active buffer layer. Different mechanisms of distributed feedback in the structure are examined. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 4, 301–305 (25 February 1997)     

The generalized Boltzmann equation

From the BBGKY-hierarchy of the kinetic equations taking into account three possible levels of scales, connected with the mean time of particle interactions, mean time between collisions and the hydrodynamic time, the generalized Boltzmann equation is derived. The generalized H-theorem is proven.     

The generalized Kolmogorov-Petrovskii-Piskunov equation

Nonlinear nonlocal equations of mathematical physics such as the K.P.P. equation, the generalized nonlinear Schrödinger equation, the Witham equation for water waves et al. are solved by decomposition.     

A generalized Vlasov equation

A two-special dimension electronic system characterized by a plasma parameter Γ 1 is analyzed; then, by using a rigorous non-equilibrium statistical mechanical theory, the evolution of distribution function is considered. A generalized Vlasov equation (GVE) is derived. Compared to the usual Vlasov equation, GVE presents an additional velocity-dependent correlation term. Taking as a starting point the GVE, the phenomenological approximation to two-particles function, ƒ₂(r₁r₂p₁p₂; t) = ƒ₁(r₁p₁;t)f₁(r₂p₂;t)g(r₁−r₂), proposed by Singwi, Tosi, Landi and Sjolander is analyzed.     

Quantum generalized Vlasov equation

An electronic system is considered as a quantum plasma characterized by a plasma parameter γ₀ 1, over short times. Using the Dynamics of Correlations (a many-body theory based on the Liouville-von Neumann equation in the Fourier transform of the Wigner-Weyl representation), in first and second order, a generalized Vlasov equation (GVE) has been derived. GVE describes as a particular situation the STLS (Singwi, Tosi, Land and Sjölander) ansatz. Discarding correlation terms in GVE, a non-linear Vlasov equation with exchange terms is derived. The classical limit and the linearization of GVE are also studied.     

Study of decoherence with a generalized master equation

The behavior of macroscopic system is investigated with a generalized master equation. Making use of a coarse-grained position operator based on the SO(3,1), we can derive that the macroscopic nature of this operator induces decoherence leading to classical behavior.     

Solitons for a generalized variable-coefficient nonlinear SchrSdinger equation

In this paper, we investigate some exact soliton solutions for a generalized variable-coefficients nonlinear SchrSdinger equation （NLS） with an arbitrary time-dependent linear potential which describes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensations. Under some reasonable assumptions, one-soliton and two-soliton solutions are constructed analytically by the Hirota method. From our results, some previous one- and two- soliton solutions for some NLS-type equations can be recovered by some appropriate selection of the various parameters. Some figures are given to demonstrate some properties of the one- and the two-soliton and the discussion about the integrability property and the Hirota method is given finally.     

New exact solitary wave solutions to generalized mKdV equation and generalized Zakharov--Kuzentsov equation

In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov--Kuzentsov equation are constructed by the method of auxiliary equation with function transformation with aid of symbolic computation system Mathematica. The method is of important significance in seeking new exact solutions to the evolution equation with arbitrary nonlinear term.