In this paper,first,by using a new transformation,the variable coefficient KdV-MKdV equation is reduced to a third-order nonlinear ordinary differential equation (NODE),and then several exact soliton-solutions for the variable coefficient KdV-MKdV equatioin are obtained through considering this NODE.The method can be also used to solve other nonlinear equations,such as the variable coefficient KP equation,sine-Gordon equation and so on.

In this paper,the nonlinear approximate equations for long wave in shallow water are studied via using two different methods.Firstly,with the aid of Mathematica and Wu-elimination method,by using sine-cosine method,three families of soliton solutions are obtained.Secondly,based on the known references,through using a new transformation,several rational formal solutions are found again.The two methods can be also applied to other nonlinear equations.

Propagation of solitons is investigated on an inhomogeneous plasmas that contain two kinds of ions with different masses.The nonlinear acoustic waves can be described by either KdV-type equation or Nonlinear Schrdinger equation in the lowest order.The amplitudes,propagating velocities or wave shapes of these quasi-solitons are analytically given in this paper.

In this paper,we obtain the general expression of the first-order correction of the Perturbation Equation of MKdV and give the exact expression of a special example.

In this paper a general approach to the Bose-Einstein condensation of neutral atoms with repellent interaction is presented.Especially in the case of free atoms (V=0) with repellent interaction,an exact solution for the atom's wave function can be derived,and therefore the calculation of atom's Bose-Einstein condensation is completed.

A four-parameter potential function is proposed.The corresponding s-wave Schrdinger equation is solved exactly,and the rotational energy is approximately considered by using a simple method.The evaluating accuracy of the potential for the experimental RKR curve and the rotational-vibrating level is far better than the usual Morse potential,and the latter is contained in this potential as a special case.

The s-wave bound states solutions of Klein-Gordon equation and Dirac equation with scalar and vector Morse-type potentials are obtained.

The equilibrium thermal radiation in a flat space-time or a curved space-time behaves like Planck black spectrum represented with coordinate quantities.We regard the fact that the radiation from a thermal equilibrium system shows Planck black spectrum as a basic physics law,from which it is demonstrated that the transitivity of clock rate synchronization is equivalent to the zeroth law of thermodynamics.The condition of clock rate synchronization is weaker than that constructing simultaneity surfaces.In the space-time satisfying the condition of clock rate synchronization,the zeroth law of thermodynamics is valid.On the other hand,in the space-time where the zeroth law is valid,one can define an identical clock rate.

It is shown that a new set of exact solutions in vacuum Brans-Dicke theory is obtained and it admits wormhole geometry.Two-way traversable wormholes in the Brans-Dicke theory is allowed for the coupling parameter ω(-2≤ω≤0) and the appropriately chosen integration constants.It also follows that the scalar field  plays the role of exotic matter and this violates the weak energy condition.

In this paper the model of two-level atomic momentum spread in amplitude-modulated standing light wave was investigated.This model shows chaotic behaviour in the classical limit.The system displays the characteristic of dynamical localization for the same parameters as those in the classical model correspoinding to it.

In this paper, the method of synchronizing chaos by driving of discrete chaotic system in continuous chaotic systems is proposed. The logistic map, Henon map and the system of Lorenz are taken as three typical examples. The simulation results show that two continuous chaotic systems can be synchronized completely when the strength of the driving signal is large enough and the spectrum of the output signal is similar to the spectrum of white noise. At the sametime, we have studied the possibility of secrete communication based on the method proposed in this paper.

Employing the intracavity absorption technique,Lamb dip of the spectrum was obtained and the resolution and sensitivity of CO Laser magnetic resonance(LMR) spectrometer was greatly improved. By this technique, the X2Π3/2(υ=1←0) Zeeman transitions of 15N16O were observed with the Λ-doubling and hyperfine structures resolved. A correlative analysis of the LMR Spectrum of 15N16O with the previous available measurements was performed. The global least-square fit provided by far the most complete and the most accurate molecular constants of all the related isotopic species of 15NmO(m=16—18). The accuracy of these constants is improved by 1 or 2 orders. Many of the molecular constants including γ, AD, Δ01, Δ10, Δ00 were determined for the first time.

The hyperfine structure of the levels 5d2D3/2 and 6p2P3/2 in BaⅡ was studied by collinear fast-ion-beam laser spectroscopy. The isotope numbers of BaⅡ in our experiment are 135 and 137, and the hyperfine structure parameters of each level are given.

Using the extened Su-Schrieffer-Heeger model and the Sum-Over-State method, we have calculated the third-order nonlinear polarizability γ and its dispersion spectra for single substitutional fullerenes C77X(X=B or N atoms). The results indicate:(1) compared with C78,each of the static values of γ through the substitutional doping increases to some extent (3—40 times);(2) the dynamic nonliear optical reponse of C77X not only depends on doping atoms, but also depends on the substituted isomers and doped sites.

By considering the detuning and the initial atomic coherence,a general expression of distance between density operators of arbitrary initial states (reference states) is obtained. The emphasize is put on the influence of detuning on the evolution in the interaction of a two-level atom of arbitrary initial states with the coherent field. The results show that the distance between density operators is obviously dependent on the value of detuning.

The atomic quantum behaviors in the system of two-mode squeezed vacuum field interacting with a two-level atom via two-photon process are studied by means of quantum theory.The condition for the occurrence of coherent trapping and the influence of the squeezing parameters on the atomic dipole squeezing are discussed.

Bright and dark spatial solitons are predicted for biased photovoltaic photorefractive crystals, which are due to both the spatially nonuniform screening of the external electric field and the photovoltaic effect. These solitons differ form previously observed photorefractive spatial solitons in their properties. When external electric field is of a certain value, these solitons may be switched from bright to dark both by changing the polarity of the external electric field and by rotating the polarization of the light. In case the effect of the external bias field is much stronger than the photovoltaic effect and the latter can be neglected, these solitons are similar to screening solitons. In case the external bias field is absent, these solitons are similar to photovoltaic solitons in the open-circuit case.

Sol-gel method was used to prepare SiO2-GeO2 films. By investigating the second-harmonic generation signal of the film after parallel plate poling and corona poling, it was found that the number of effective dipoles in the sample increased with the plate poling voltage. A model of the release of effective dipoles was proposed to explain the super-quadratic relation between the second-order nonlinearity and the poling voltage.

Based on Jacobson's molecular free length theory in lipuids and the relationship between the ultrasonic velocity and the molecular free length in organic lipuids, the eqution of temperature coefficient of ultrasonic velocity in organic liquid binary mixtures is derived. The calculated temperature coefficients of ultrasonic velocity are in good agreement with the measured results.

Based on Jacobson's molecular free length theory in lipuids and the relationstip between the ultrasonic velocity and the molecular free length in organic liquids, the equation of pressure coefficient of ultrasonic velocity in organic liquid binary mixtures is derived. The calculated pressure coefficients of ultrasonic velocity are in good agreement with the measured results.

Flattened carbon nanoshells,carbon nanorods, and nanostructures of rod-tube have been observed in the cathodic doposits produced by a double-anode arc-discharge. As confirmed by high resolution transmission electron microscope (HRTEM), the growth of a carbon nanotube was directly linked to the nanorod, so the origin and development of nanotube seed is clearly discernible. In addition, the multishelled carbon nanorods HRTEM images revealed an isolated center line. We consider that such a line is probably a linear acetylenic carbon allotrope based on “sp” hybridization containing triple and single bonds.

Non-crystalline alloys can be turned into nano-crystalline under shock waves. This has been proved by our experiments.Recently,we have discovered that the functions of Cu and Nb of Fe73.5Cu1Nb3B9Si13.5 in shock wave crystallization are restrained, and the size of crystallites in the crystallized alloy Fe73.5Cu1Nb3B9Si13.5 is increased and its lattice constant is decreased after the sample is annealed again. These phenomena are worth to study further. The model of fluid-change for explaining the law of shock wave crystallization is suggested in this paper.

The effect of atomic hydrogen on C2H2-covered Si surface was studied by high resolution electron loss spectroscope and low energy electron diffraction, the findings was that atomic hydrogen broke up C—C bond in C2H2 and the Si—Si dimer to form C—H，Si—H respectively. According to experimental phenomena, several cluster models were devised for quantum chemistry calculation. The calculation results agreed to experiment well and the discussions on the reaction sites of C2H2 adsorbed on Si(100) surface and the role of atomic hydrogen and nucleation mechanisn of diamond hetereopitaxy on Si were performed.

In external electrical field,the self-trapping biexciton in non-degenerate ground state conjugated polymer has an abnormal characteristic-its static polarizability was found to be negative.We calculated the dynamic response function χ(ω) of biexciton.By putting ω to the zero limit,we got the static polarizability χ which proved to be negative.We compared it with that of self-trapping exciton and ground state and gave some analysis on the origin of negative polarizability.Finally,we investigated the behavior of χ(ω) when ω is small,and deduced that if more biexcitons are excited,the n(ω) of the material will decrease,whereas if more excitons are excited,the n(ω) will increase.

Taking into account the scattering from bulk impurities and rough interfaces,we use the quantum-statistical Greens function approach and Kubo theory to calculate the one-particle Greens function and the conductivity in a magnetic multilayered metallic system.It is found that the conductivity depends on both the spatial size and the amplitudes for the reflected waves by the interfaces,and exbibits the main features of the giant magnetoresistance experiment.

The formation and propagation of domains in superlattices are discussed using a nonlinear Schrdinger equation.Negative differential conductivity in superlattices leads to the growth of inevitable spatial fluctuations,and a propagating electron accumulation-layer domain is formed.It is shown that envelopes of the wave functions are governed by the nonlinear Schrdinger equation which has soliton solutions.

In this paper,a renormalization group scheme within the framework of the mean field theory is used to investigate the critical behavior at the surface of a semi-infinite Ising system with mixed spins,i.e.,S=1 at the surface and σ=1/2 in the bulk.The effects of the random field and amorphism on the surface phase diagrams are obtained and discussed.The numerical results show that the surface tricritical points and reentrant phenomena exist due to the competition between the surface random field and certain magnitude of surface amorphization.

A series of polycrystal samples of La0.75Ca0.25-xSrxMnO3(x=0,0.075,0.1，0.125，0.14，0.15，0.175，0.2，0.25)was prepared.The entropy change and Curie temperature were measured under a magnetic field 1.5T.The microstructure of samples was used to explain the change of properties as Sr2+ substituted for Ca2+.Amalgamating a few of samples made the compound material suitable to employ Ericsson cycle.

We introduce a phenomelogical model to describe the characters of ferroelectric superlattices.Three kinds of coupling ways are considered in the model.The polarization,Curie temperature and the critical size of the superlattices are obtained by computational simulation.We think that the coupling coefficients are functions related with the temperature and the lattice size.An experience formula is introduced to explain recent experimental results about the KTaO3/KNbO3 superlattice material.

A new kind of Fe nanowire array was successfully prepared by electrochemical deposition in nanoporous anodic aluminum oxide(AAO)template.Its micrography and crystalloid structure was investigated by transmission electron microscopy and electron diffraction.The results indicated that the nanowires in the array are very uniform and well isolated,and parallel to each other.Each nanowire appeared as a chain of peanuts,and the particle in this chain was proposed to be a single crystal of α-Fe. Its magnetic anisotropy was characterized by using Vibrating Sample Magnetometer(VSM) and Mssbauer spectrum(MS).The VSM results clearly revealed that the α-Fe nanowire array in the alumite shows a strong perpendicular magnetic anisotropy with the easy direction normal to the alumite.And the perpendicular hysteresis loops curve has high squareness (0.98) and coercive force (1.76×105A/m).The MS proved that the moment of each nanowire in AAO template is highly orientated along its axis and perpendicular to the surface of the membrane. The saturation magnetization (Ms)of the nanowire array is similar to that of the bulk materials(0.17T).