In this paper, we make use of a new generalized ansatz in the homogeneous balance method, the well-known Riccati equation and the symbolic computation to study a generalized Hirota--Satsuma coupled KdV system and a coupled MKdV equation, respectively. As a result, numerous explicit exact solutions, comprising new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions, are obtained.

In this paper, a variable separation approach is used to obtain
localized coherent structures of the (2+1)-dimensional generalized nonlinear Schrodinger equation:$\i\varphi_t-(\alpha \beta)\varphi_{xx}+(\alpha+\beta)\varphi_{yy}-2\lambda \varphi
\bigg[(\alpha+\beta)\bigg(\dint_{-\infty}^x|\varphi|_{y}^2\dd x+u_1(y,t)\bigg) $$-(\alpha-\beta)\bigg(\dint_{-\infty}^y|\varphi|_{x}^2\ddy+u_2(x,t)\bigg)\bigg]=0.$
By applying a special B\"{a}cklund transformation and introducing arbitrary functions of the seed solutions, the abundance of the localized structures of this model are derived. By selecting the arbitrary functions appropriately, some special types of localized excitations such as dromions, dromion lattice, breathers and instantons are constructed.

An analysis of the chaos suppression of a nonlinear elastic beam (NLEB) is presented. In terms of modal transformation the equation of NLEB is reduced to the Duffing equation. It is shown that the chaotic behaviour of the NLEB is sensitively dependent on the parameters of perturbations and initial conditions. By adjusting the frequency of parametric perturbation to twice that of the periodic one and the amplitude of parametric perturbation to the same as the periodic one, the chaotic region of the nonlinear elastic beam driven by periodic force can be greatly suppressed.

Some sufficient criteria have been established to ensure the global exponential stability of delayed cellular neural networks by using
an approach based on delay differential inequality. Compared with
the method of Lyapunov functionals as in most previous studies, our
method is simpler and more effective for a stability analysis of
delayed system. Some previously established results in the
literature are shown to be special cases of the present result.

The white-gain model and the white-loss model of a single-mode laser are investigated in the presence of cross-correlations between the real and imaginary parts of quantum noise as well as pump noise. It was found that, like the white cubic model (2001 Chin. Phys. Lett. 18 370), the amplitude equations are all decoupled from the phase equations for the two models, and the same novel term appears in the amplitude equations of the two models. So we can put the amplitude equations of all the models
into a general form, that is, the new amplitude equation. We further use this new amplitude equation to study specifically the stationary properties of the laser intensity for the white-gain model.

We propose a new four-level atomic model for achieving light
amplification at a short wavelength, where direct incoherent
pumping into the top level is avoided by the advantage of
coherent pumping. In this model, the lower level of the probe
transition is an excited state but not the usual ground state.
By analytical as well as numerical calculations, we find that the
probe gain, either with or without population inversion, which depends
on the relation between spontaneous decay rates $\g_{42}$ and $\g_{21}$, can be achieved with proper parameters. We note that the Raman scattering
gain always plays an important role in achieving the probe amplification.

The dissipation of the field in the two-photon Jaynes--Cummings model (JCM) with degenerate atomic levels was studied. The initial degenerate atomic state affects the field coherence loss. When the degenerate atom is initially in an equal probability superposition state, the field coherence loss is smallest. It is found that the degeneracy of the atomic level increases the period of entanglement between the atom and the field. When the degeneracy was considered, the coherence properties of the field could be affected by the reservoir qualitatively, if a nonlinear two-photon process is involved. This is different from the dissipation of one-photon JCM with degenerate atomic levels.

We propose a quantum nondemolition measurement of the photon-number
distribution for a weak cavity field with no more than two photons. The
scheme is based on the resonant interaction of atoms with the cavity
field, and thus the required interaction time is much shorter than that using dispersive interaction. This is important in view of decoherence. Our scheme can also be used to generate even and odd coherent states for a weak cavity field with resonant atoms.

Theoretical studies and analytical scalings were carried out to find the optimized laser parameters and target conditions so that ultrashort hard x-ray pulses and high x-ray power could be achieved. The dependence of laser intensity and wavelength on the yield of $K$-shell x-ray emission was studied. We propose an optimal design for a foil target for producing high-yield hard x-ray pulses of customizing duration.

In this paper, incompressible, double-diffusive convection is simulated
using finite-difference schemes. The Navier--Stokes equations are
expressed in terms of stream function and vorticity. Because of
the existence of large velocity, temperature and salinity gradients
in boundary layers, a boundary-fitted coordinate system is used
to concentrate the grid points near the wall and fit complex
boundaries. The finite-difference methods used include the high-order
accurate upwind difference scheme. It is
shown that the scheme is a good candidate for direct simulations of
double-diffusive convection flows. The proposed method is first
applied to symmetry breaking and overturning states in
thermohaline-driven flows in trapezoid basins. The basic phenomena
agree well with those by Dijkstra and Molemaker (1997 {\em J. Fluid
Mech.} {\bf 331} 169)
and Quon and Ghil (1992 {\em J. Fluid Mech.} {\bf 245} 449), but symmetry breaking and
overturning states can occur in an asymmetric geometrical region
without perturbations. Then the method is applied to double-diffusive
convections in a cavity with opposing horizontal temperature and
concentration gradients at large thermal ($Rt$), solutal ($Rs$)
Rayleigh numbers and Lewis number. There are three straight sides
and a sine curve side in the cavity. Basically, numerical results
are in agreement with those of Lee and Hyun (1990 {\em Int. J. Heat
Mass Transfer} {\bf 33} 1619) qualitatively, but eddies mixing in the
top left-hand corner near the curved wall affects the layered structure.

The confined flow around a square cylinder mounted inside a
two-dimensional channel (blockage ratio $\be=1/8$) was investigated in
detail by a newly developed incompressible nonuniform lattice-BGK
model. It is found that the vortex shedding behind the cylinder
induces periodicity in the flow field, and the periodicity of the
flow will lose for $Re>$300. A detailed analysis for a range of
Reynolds numbers between 1 and 500 was presented. Quantitative
comparisons with other methods show that the model gives accurate
results for complex flows.

The equivalence between the Bargmann--Wigner (B-W) equations and the
Klein--Gordon (K-G) equations for integral spin, and the Rarita--Schwinger (R-S) equations for half integral spin is established by explicit derivation, starting from the lowest spin cases. It is demonstrated that all the constraints or subsidiary conditions imposed on the K-G or R-S equations are included in the B-W equations.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

The excimer laser-induced crystallization technique has been
used to investigate the preparation of nanocrystalline silicon (nc-Si)
from amorphous silicon ($\al$-Si) thin films on silicon or glass
substrates. The $\al$-Si films without hydrogen grown by pulsed-laser
deposition are chosen as precursor to avoid the
problem of hydrogen effluence during annealing. Analyses
have been performed by scanning electron microscopy, atomic
force microscopy, Raman scattering spectroscopy and high-resolution
transmission--electron microscopy. Experimental results show
that silicon nanocrystals can be formed through laser annealing.
The growth characters of nc-Si are strongly dependent on the laser
energy density. It is shown that the volume of the molten silicon
predominates essentially the grain size of nc-Si, and the surface
tension of the crystallized silicon is responsible for the mechanism of nc-Si growth.

A two-dimensional (2D) binary system without considering the Lennard-Jones (L-J) potential has been studied by using the Collins model. In this paper, we introduce the L-J potential into the 2D binary system and consider the existence of the holes that are called the ``molecular fraction". The liquid--gas phase diagram of the 2D alternative binary L-J system is obtained. The results are quite analogous to the behaviour of 3D substances.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

The defects associated with lead vacancies ($V_{\rm Pb}$) in lead tungstate crystals (PbWO$_4$) are investigated by the relativistic self-consistent discrete variational embedded cluster method. We focus on the density of states and the effect of $V_{\rm Pb}$ on surroundings.
The results show that the existence of $V_{\rm Pb}$ can diminish the bandwidth of WO$_4^{ \ 2-}$ group, however, it can neither produce O$^-$ and Pb$^{3+}$ ions nor result in absorptions at 350 and 420\,nm. The charge balance of $V_{\rm P\!b}$ may be evenly compensated by the surrounding oxygen ions.

The effects of incomplete ionization of nitrogen in 4H-SiC have
been investigated. Poisson's equation is numerically analysed by
considering the effects of Poole--Frenkel, and the effects of
the potential on $N^+_\dd$ (the concentration of ionized donors)
and $n$ (the concentration of electrons). The pinch-off voltages
of the uniform and the ion-implanted channels of 4H-SiC
metal-semiconductor field-effect transistors (MESFETs) and
the capacitance of the gate are given at different temperatures.
Both the Poole--Frenkel effect and the potential have influence on
the pinch-off voltage $V_{\rm p}$ of 4H-SiC MESFETs. Although the
$C$-$V$ characteristics of the ion-implanted and the uniform channel of
4H-SiC MESFETs have a clear distinction, the effects of incomplete
ionization on the $C$-$V$ characteristics are not significant.

Based on the MIS model, a simple method to extract parameters of
SiC Schottky diodes is presented using the $I$-$V$ characteristics.
The interface oxide capacitance $C_\i$ is extracted for the first time,
as far as we know. Parameters of 4H-SiC Schottky diodes fabricated
for testing in this paper are: the ideality factor $n$, the series
resistance $R_{\rm s}$, the zero-field barrier height $\phi_{\rm B0}$,
the interface state density $D_{\rm it}$, the interface oxide
capacitance $C_\i$ and the neutral level
of interface states $\phi_0$.

1.3 um emitting InAs/GaAs quantum dots (QDs) have been grown by molecular beam epitaxy and QD light emitting diodes (LEDs) have been fabricated. In the electroluminescence spectra of QD LEDs, two clear peaks corresponding to the ground state emission and the excited state emission are observed. It was found that the ground state emission could be achieved by increasing the number of QDs contained in the active region because of the state filling effect. This work demonstrates a way to control and tune the emitting wavelength of QD LEDs and lasers.

Metal-coated nanoshell, the nanoparticle consisting of a nanometre-scale dielectric core coated with a thin metallic shell, exhibits three distinct optical resonant forms, the sphere cavity resonance (SCR), plasmon resonance (PR), and concentric dielectric sphere resonance (CDSR). The SCR, PR and CDSR of the metal-coated nanoshell reveal a geometric tunability controlled by the core radius and by the ratio of the core radius to the total radius. Classical electrodynamics and Mie scattering theory are used to treat the resonant forms and the transition state between the resonant forms. Based on previous experimental research, we present a group of resonant equations for all the resonant forms, which depend on the geometric structure of the metal-coated nanoshell.

In this paper, we discuss the phase-change recording at a short-wavelength (514nm) and a high numerical aperture (0.85). Effects
of recording power and pulse width on the size of the recording
marks are studied. The minimum recording mark with a length of
approximately 220nm has been observed. The capacity of about 17GB
for a single-layer disc of a 12cm diameter can be obtained. The
maximum carrier-to-noise ratio reaches 45dB at a writing power of 13--14mW.