SYMMETRIES AND DROMION SOLUTION OF A (2+1)-DIMENSIONAL NONLINEAR SOHR?DINGER EQUATION

The Painlevé property, infinitely many symmetries and exact solutions of a (2+1)-dimensional nonlinear Schr?dinger equation, which are obtained from the constraints of the Kadomtsev-Petviashvili equation, are studied in this paper. The Painlevé property is proved by the Weiss-Kruskal approach, the infinitely many symmetries are obtained by the formal series symmetry method and the dromion-like solution which is localized exponentially in all directions is obtained by a variable separation method.     

A DIRECT PERTURBATION THEORY OF THE NONLINEAR SCHR?DINGER EQUATION WITH CORRECTIONS

An exact direct perturbation theory of nonlinear Schrodinger equation with corrections is developed under the condition that the initial value of the perturbed solution is equal to the value of an exact multisoliton solution at a particular time. After showing the squared Jost functions are the eigenfunctions of the linearized operator with a vanishing eigenvalue,suitable definitions of adjoint functions and inner product are introduced. Orthogonal relations are derived and the expansion of the unity in terms of the squared Jost functions is naturally implied. The completeness of the squared Jost functions is shown by the generalized Marchenko equation. As an example,the evolution of a Raman loss compensated soliton in an optical fiber is treated.     

CONSTRUCTION OF THE SOLITON STATES OF THE QUANTUM NONLINEAR SCHR?DINGER EQUATION

The quantum nonlinear schr?dinger equation (QNSE) is exactly solved by Beth's ansatz method and we give a reasonable definition of the quantum soliton states. From the definition we construct the soliton states of the QNSE from its bound-state solutions. The dispersion effect of the quantum soliton is also exactly analysed.     

CONSTRUCTION OF THE SOLITON STATES OF THE QUANTUM NONLINEAR SCHR?DINGER EQUATION

The quantum nonlinear schr?dinger equation (QNSE) is exactly solved by Beth's ansatz method and we give a reasonable definition of the quantum soliton states. From the definition we construct the soliton states of the QNSE from its bound-state solutions. The dispersion effect of the quantum soliton is also exactly analysed.     

THE NONLINEAR SCHR?DINGER EQUATION AND THE CROSS-PHASE MODULATION IN ERBIUM-DOPED FIBER AMPLIFIERS

The nonlinear Schr$\ddot{o}$dinger equation(NLSE) in erbium-doped fiber(EDF) was obtained. The cross-phase modulation (XPM) in the erbium-doped fiber amplifiers (EDFA) was studied based on this NLSE and the rate equations. A more generalized form of the propagation equation in EDFA was obtained which included the phase shifts the EDFA induced. An analytical expression was given to the XPM in the EDFA. It was found that the XPM in the EDFA dose not change very much with the wavelength except at the neighboring wavelengths (around 1531 nm) where the absorption and emission cross-sections of the erbium ions reach their maxima, and the XPMs have opposite signs on the two sides around 1531 nm. Furthermore, it was found that the XPM increases with the increase of the length of EDF.     

A SOLITON PERTURBATION THEORY FOR THE UNSTABLE NONLINEAR SCHR?DINGER EQUATION WITH CORRECTIONS

Based on the Zakharov-Shabat equation of the inverse scattering transform for the unstable nonlinear Schr?dinger equation, for which a perturbation theory with corrections is developed in this paper. All necessary formulae for calculating the scattering data are derived. Based upon these formulae, the effect due to the corrections can be studied. As an example, the correction due to the damping is calculated.     

ON THE APPLICATION OF A GENERALIZED VERSION OF THE DRESSING METHOD TO THE INTEGRATION OF VARIABLE COEFFICIENT N-COUPLED NONLINEAR SCHRÖDINGER EQUATION

N-coupled nonlinear Schrödinger (NLS) equations have been proposed to describe N-pulse simultaneous propagation in optical fibers. When the fiber is nonuniform, N-coupled variable-coefficient NLS equations can arise. In this paper, a family of N-coupled integrable variable-coefficient NLS equations are studied by using a generalized version of the dressing method. We first extend the dressing method to the versions with (N + 1) × (N + 1) operators and (2N + 1) × (2N + 1) operators. Then, we obtain three types of N-coupled variable-coefficient equations (N-coupled NLS equations, N-coupled Hirota equations and N-coupled high-order NLS equations). Then, the compatibility conditions are given, which insure that these equations are integrable. Finally, the explicit solutions of the new integrable equations are obtained.     

THE BETHE-SALPETER EQUATION FOR SPIN (0—3/2) ELECTROMAGNETIC BOUND SYSTEM AND ITS APPROXIMATE SOLUTION

In this paper. the Bethe-Salpeter equation for spin (0—3/2) electromagnetic bound system is derived. Under the ladder approximation the approximate B-S wave function with accuracy up to order 0(α) for this system is obtained. Utilizing this wave function, we estimated the cross section for producing (π⁺Ω^－) in Ω^－-p collision process.     

A RELATIVISTIC EQUATION OF MOTION FOR MANY-BODY SYSTEM(Ⅱ)

A relativistic equation of motion for many-body system is established. The relativistic potential is a certain rearrangement of the irreducible series of many-body B-S equation. Considering the two-body irreducible B-S kernels only the many-body potential is expressed as a sum of two-body ones.     

A STUDY OF RAMAN SCATTERING AND INFRARED ABSORPTION SPECTRUM IN A NEW SERIES OF MERCURY-BASED HIGH-Tc SUPERCONDUCTOR (Hg,Mo)Sr2(Y1-xCax)Cu2O6+δ

Lattice vibrations of the (Hg,Mo)Sr₂(Y_1-xCa_x)Cu₂O_6+δ—a new series of mercury-based high-T_c superconductor are analyzed with the aid ofgroup theory. The vibrations of species are given. They are 4A_1g+ B_1g+ 5E_g+ 7A_2u + B_2u+ 8E_u. The 4A_1g, B_1g and 5E_g modes are Ramma active, the 6A_2u and 7E_u are infrared active. Phonon vibration characteristics of the samples are studied using Raman scattering and infrared absorption spectra. The experimental results show that the typical phonon vibrational modes appear mainly at 145, 320, 440, 578, 592 and 645cm^-1, The intensities of the 145, 320, 440, 578 and 645 peaks decrease with increasing Ca content x and the position of 645 peak moves to higher wavenumber slightly. In this article, the phonan modes are assigned and their variation behavior with increasing Ca content x are discussed.     

MEASUREMENTS OF NUMBER OF RADIOACTIVE ATOMS AND HALF-LIFE(Ⅲ)

The present paper examines theoretically the way of reducing tha errors introducedby the inaccuracy of the decay constant and measuring statistics in the determinationof the number of the radioactive atoms. It was discovered that the "front-back sym-metrical measurements with life-time as center" (FBSLC) may fulfil this reguirement.Even if the error of the decay constant reaches ±10%, the error introdnced by theinaccuracy of decay constant of the number of the radioactive atoms at zero time cal-culated from the radioactivities measured at zero time and two life-times by takingaverage will still be smaller than 0.1%. Experimental data of ^99mTc radioactive decaywithin measuring statistics verified the above theoretical prediction. Therefore, by FBSLC with measuring time as early as possible, it is possible toreduce the errors introduced by inaccuracy of the decay constant and measuring sta-tistics, so that the results of the absolute measurements may be more accurate.     

ELECTRON MOMENTUM SPECTRA OF EXCITED He(2~1S) AND He(2~3S)

ＥＬＥＣＴＲＯＮＭＯＭＥＮＴＵＭＳＰＥＣＴＲＡＯＦＥＸＣＩＴＥＤＨｅ（２１Ｓ）ＡＮＤＨｅ（２３Ｓ）ＣｈｅｎＺｈａｎｇｊｉｎＳｈｉＱｉｃｕｎＣｈｅｎＪｉＸｕＫｅｚｕｎＤｅｐａｒｔｍｅｎｔｏｆＭｏｄｅｒｎＰｈｙｓｉｃｓ，ＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎ...     

(1/2+1/2+1)腔型热阴极微波电子枪

 介绍了一种新型的轴耦合热阴极微波电子枪的设计，该枪采用了缩短首腔以及在首腔与主加速腔间插入耦合半腔的设计思想，在不破坏粒子束性能的基础上尽量减小反轰功率，给出了用Superfish 及Pamela软件进行物理设计以及粒子动力学计算的结果，在脉冲宽度为6μs, 重复频率为25Hz时，阴极上平均反轰功率为3.6W,达到设计要求。     

(1/2+1/2+1)腔型热阴极微波电子枪

介绍了一种新型的轴耦合热阴极微波电子枪的设计,该枪采用了缩短首腔以及在首腔与主加速腔间插入耦合半腔的设计思想,在不破坏粒子束性能的基础上尽量减小反轰功率,给出了用Superfish 及Pamela软件进行物理设计以及粒子动力学计算的结果,在脉冲宽度为6μs, 重复频率为25Hz时,阴极上平均反轰功率为3.6W,达到设计要求。     

THEORETICAL ASPECTS OF ELECTRON CAPTURE BY C~(6 ) AND O~(8 ) FROM H,He AND H_2

Many theoretical approaches to electron capture by C~(6 ), a nd O~(8 ) fromthe targets H,He and H_2 are discussed from the practical stand point at thepresent stage.The validity of several representative methods for the calcul-ation of total and state selective partial cross sections is given. For the total cross section in many theoretical methods can be appliedand give reasonable results.For the state selective partial cross section for adominant channel at low impact velocities manylevel coupled channel calcul-ations can be used and give reliable results,if it belongs to a dominant cha-nnel.     

DISCUSSION OF A SU(2)×U(1)×S3 MODEL WITH TWO HIGGS DOUBLETS AND CALCULATION OF CABIBBO-LIKE-PARAMETERS

In this paper a SU(2)×U(1)×S₃ model with two Higgs doublets is discussed in detail. It is shown that besides the case discussed by Segre et al., there is another physically interesting case. We investigate the latter in detail. In This case, taking the quark masses and the Cabibbo angle θ₁ as input parameters, we can obtain Cabibbo angles θ₂ and θ₃ which have the same order of magnitude as θ₁. Finally the appearance of a pseudo Goldstone boson in the model is discussed, a method to overcome the difficulty is given, and the physical results of this case which do not contradict with the experiments are discussed.     

Structure and stability of SiBn+ AND CBn+ (n = 1–4)

The structures and binding energies of small boron-rich clusters are studied using correlated wave functions and polarization basis sets. Carbon is the central atom in CB_n⁺, while SiB_n⁺ prefers planar boron networks with silicon as one of the edge atoms. These ground state structures can be explained by differences in the electronegativities of the component elements. The various fragmentation channels of SiB_n⁺ are also examined using binding energy differences.     

STATICAL SPHEROSYMMETRICAL SOURCELESS SOLUTION OF SU(2) GAUGE FIELD——THE SELFDUALITY,UNIQUENESS AND THE SELF INDUCED CHARGE CURRENT

It is shown that the statical spherosymmetrical sourceless solutions of SU(2) guagefield,which satisfy a physical boundary condition,must be selfdual.Then from theselfdual condition,we solve the equation explicitily,hence show the uniqueness analy-tically.By gauge transforming the Lagrangian by a local generator of synchrono-symmetry,we get a corresponding local charge current density,which is both gaugeinvariant and conserved.The total values of either electric or magnetic charge arequantized,but the charge distributions in space are continuous and not restrictedby quantization.Finally we discuss a mechanism of spontaneous symmetry break-down.Contrary to ordinary magnetic flux string,now the ordered phase is surround-ed by the normal phase,the ordered phase repels electric fields,and electric fieldsdestory the ordered phase.