Approximate Symmetry Reduction to the Perturbed One-Dimensional Nonlinear Schrödinger Equation

The one-dimensional nonlinear Schrödinger equation with a perturbation of polynomial type is considered. Using the approximate symmetry perturbation theory, the approximate symmetries and approximate symmetry reduction equations are obtained.     

Two-dimensional discrete gap breathers in a two-dimensional discrete diatomic Klein-Gordon lattice

We study the existence and stability of two-dimensional discrete breathers in a two-dimensionai discrete diatomic Klein-Gordon lattice consisting of alternating light and heavy atoms, with nearest-neighbor harmonic coupling. Localized solutions to the corresponding nonlinear differential equations with frequencies inside the gap of the linear wave spectrum, i.e. two-dimensional gap breathers, are investigated numerically. The numerical results of the corresponding algebraic equations demonstrate the possibility of the existence of two-dimensional gap breathers with three types of symmetries, i.e., symmetric, twin-antisymmetric and single-antisymmetric. Their stability depends on the nonlinear on-site potential （soft or hard）, the interaction potential （attractive or repulsive） and the center of the two-dimensional gap breathers （on a light or a heavy atom）.     

Multi-Soliton Solutions of the Levi Equations

The multisoliton solutions of the Levi equations are derived with the Hirota method and Wronskian technique respectively.     

Effect of Local Magnetic Field in G Measurement with Time-of-Swing Method

The effect of the local time- varying magnetic field in our G measurement with the time-of-swing method is studied by magnifying the magnetic field to cause a perceptible change in the pendulum＇s period. The experimental result shows that the coefficients of the change in the period to the magnetic field are 37（1） and 12（1） ms/gauss in the two horizontal directions respectively, which means that the systematic uncertainty due to the local magnetic field is less than 0.4ppm in our G measurement.     

A new construction of quasi-solvable quantum many-body systems of deformed Calogero-Sutherland type

We make a new multivariate generalization of the type A monomial space of a single variable. It is different from the previously introduced type A space of several variables which is an sl(M+1) module, and we thus call it type A′. We construct the most general quasi-solvable operator of (at most) second-order which preserves the type A′ space. Investigating directly the condition under which the type A′ operators can be transformed to Schrödinger operators, we obtain the complete list of the type A′ quasi-solvable quantum many-body systems. In particular, we find new quasi-solvable models of deformed Calogero-Sutherland type which are different from the Inozemtsev systems. We also examine a new multivariate generalization of the type C monomial space based on the type A′ scheme.     

A quantum long time energy red shift: a contribution to varying <Emphasis Type="Italic">α</Emphasis> theories

By analyzing the survival probability amplitude of an unstable state we show that the energy corrections to this state in the long (t→∞) and relatively short (lifetime of the state) time regions are different. It is shown that in the considered model the above corrections decrease to zero as t→∞. It is hypothesized that this property could be detected by analyzing the spectra of distant astrophysical objects. The above property of unstable states may influence the measured values of possible deviations of the fine structure constant α as well as other astrophysical and cosmological parameters.     

Bose-Einstein solitons in time-dependent linear potential

In this paper, Bose-Einstein soliton solutions of the nonlinear Schrödinger equation with time-dependent linear potential are considered. Based on the F-expansion method, we present a number of Jacobian elliptic function solutions. Particular cases of these solutions, where the elliptic function modulus equals 1 and 0, are various localized solutions and trigonometric functions, respectively. Specially, for V_ext = ZF(T) = Z[mg + Hcos (ω₁T)], we discussed the Bose-Einstein condensate trapped in the coupling external field with considering the effect of gravity; for F(T) = constant, it describes the wave (Langmuir or electromagnetic) in a linearly inhomogeneous plasma with cubic nonlinearly.     

Texture formation in polycrystalline diamond vapour growth under the influence of a pulsed supersonic beam

Polycrystalline diamond film deposition is studied under the influence of a pulsed supersonic beam. The beam is formed by a high-pressure value which is used as gas inlet in an otherwise conventional hot-filament reactor. The growth rate of the films as well as the typical size of the microcrystallites are independent of the stagnation pressure behind the nozzle of the valve as long as the background pressure and the gas flow through the chamber are kept constant. In contrast, a drastic change in texture formation is found.     

Abundant multisoliton structures of the Konopelchenko-Dubrovsky equation

Using the homogenous balance method, the nonlinear transformations of the (2+1)-dimensional integrable Konopelchenko-Dubrovsky equation are given, and then some new special types of single solitary wave solution and the multisoliton solutions are constructed. The project is supported by the Natural Science Foundation of Shandong Province in China and the Natural Science Foundation of Liaocheng University.     

The measurement of the electronic g-factor in hydrogen-like ions --A promising tool for determining fundamental and nuclear constants

We describe a double-Penning-trap experiment suitable for testing QED in strong fields by determining the electronic g-factor of a single hydrogen-like ion in its ground state. Our measurements on ¹²C^{5 +} reach a relative accuracy of 2×10^-9, where the largest uncertainty results from the mass of the electron. Together with equally precise theoretical predictions therefore, it is possible to evaluate a new value for the electron's mass. The possibilities to obtain other fundamental constants and nuclear parameters are lined out. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: t.beier@gsi.de