A Series of Variable Separation Solutions and New Soliton Structures of （2＋1）-Dimensional Korteweg-de Vries Equation

Variable separation approach is introduced to solve the （2＋1）-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model （24）. Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately.     

GENERALIZED GREEN''''S FUNCTIONS OF SURFACE EXCITATION OF ELASTIC WAVE FIELDS IN A PIEZOELECTRIC HALF-SPACE

Since the generalized Green's functions,which correspond to surface excitation of elastic wavefields in a half-space of piezoelectric crystal,are independent of excitation conditions and only depen-dent on material parameters and orientation,they can be investigated in advance and independently. It is shown that the generalized Green's functions can be written as a sum of three parts repre-senting separately a surface wave,a bulk wave and an electrostatic effect. We also confirm that the surface wave part and the bulk wave part at the far field of the generalizedGreen's functions can be expressed by analytical expressions,and thus,the surface wave field and thefar field of bulk wave among the excited elastic wave fields can be evaluated exactly. Finally,as an example,the generalized Green's functions for the 6 mm crystal are given.     

Functional Integrals and Excitation Energy in Three-Band Hubbard Model

The normal and anomalous Green＇s functions of antiferromagnetie state in three-band Hubbard model are studied by using functional integrals and temperature Green＇s function method. The equations of energy spectrum are derived. In addition, excitation energy of Fermi fields are calculated under long wave approximation.     

New exact excitations and soliton fission and fusion for the （2＋1）-dimensional Broer-Kaup-Kupershmidt system

With the help of an extended mapping approach, a series of new types of exact excitations with two arbitrary functions of the (2 1)-dimensional Broer-Kaup-Kupershmidt (BKK) system is derived. Based on the derived solitary wave excitation, some specific soliton fission and fusion solutions of the higher-dimensional BKK system are also obtained.     

Production mechanism of superheavy nuclei in massive fusion reactions

Within the concept of the dinuclear system (DNS), a dynamical model is proposed for describing the formation of superheavy nuclei in complete fusion reactions by incorporating the coupling of the relative motion to the nucleon transfer process. The capture of two heavy colliding nuclei, the formation of the compound nucleus and the de-excitation process are calculated by using an empirical coupled channel model, solving a set of microscopically derived master equations numerically and applying statistical theory, respectively. Fusion-fission reactions and evaporation residue excitation functions of synthesizing superheavy nuclei (SHN) are investigated systematically and compared them with available experimental data. The possible factors that affecting the production cross sections of SHN are discussed in this workshop.     

Production mechanism of superheavy nuclei in massive fusion reactions

Within the concept of the dinuclear system (DNS), a dynamical model is proposed for describing the formation of superheavy nuclei in complete fusion reactions by incorporating the coupling of the relative motion to the nucleon transfer process. The capture of two heavy colliding nuclei, the formation of the compound nucleus and the de-excitation process are calculated by using an empirical coupled channel model, solving a set of microscopically derived master equations numerically and applying statistical theory, respectively. Fusion-fission reactions and evaporation residue excitation functions of synthesizing superheavy nuclei (SHN) are investigated systematically and compared them with available experimental data. The possible factors that affecting the production cross sections of SHN are discussed in this workshop.     

Influence of Excitation Pulse Width on the Second-Order Correlation Functions of the Exciton-Biexciton Emissions

We investigate theoretically the population dynamics and the second-order correlation functions of photon emissions from the biexciton-exciton system of a single quantum dot with excitation from pulses to continuous wave. The dynamic equations of the correlation functions are deduced by applying quantum regression theorem to optical Bloch equations. The influences of excitation pulse width on the correlation function have been discussed in detail.     

More Detailed Study of Deformation Effects in Prescission Particle Emission by a Diffusion Model

Deformation effects on particle emission in a fission process of ^251Es nucleus as functions of excitation energy, angular momentum, and viscosity coefficient have been investigated in detail within the framework of Smolu-chowski equation. Our calculations show that high excitation energy, low angular momentum, and large viscosity will enhance the influence of deformation on multiplicity of prescission particles, and that the roles of these three parameters will become weak with decreasing deformation.     

Fusion and fission solitons for the (2+1)-dimensional generalized Breor-Kaup system

With a projective equation and a linear variable separation method, this paper derives new families of variable separation solutions (including solitory wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for (2+1)-dimensional generalized Breor-Kaup (GBK) system. Based on the derived solitary wave excitation, it obtains fusion and fission solitons.     

Excitation spectrum and structure factor of a two-component Bose-Einstein condensate in different hyperfine states

The elementary excitation spectrum of a two-component Bose-Einstein condensate in different hyperfine states is obtained by Green＇s function method. It is found to have two branches. In the long wave-length limit, the two branches of the excitation spectrum are reduced to one phonon excitation and one single-particle excitation. The single-particle one has an energy gap. When the energy gap exists, we study the Landau critical velocity and the depletion of the condensate. With the obtained Green＇s functions, we calculate the structure factor of a two-component condensate. It is found that the static structure factor comprises only the branch of the phonon excitation and the single-particle excitation makes no contribution to the structure factor.     

Nonpropagating Solitons in (2+1)-Dimensional Dispersive Long-Water Wave System

With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc. are revealed by selecting appropriate functions in this paper.     

Backlund Transformations for the Initial Problems of Nizhnich and Nizhnich-Novikov-Veselov Equations

The homogeneous balance method is a method for solving general partial differential equations (PDEs). Inthis paper we solve a kind of initial problems of the PDEs by using the special Backlund transformations of the initialproblem. The basic Fourier transformation method and some variable-separation skill are used as auxiliaries. Two initialproblems of Nizhnich and the Nizhnich-Novikov-Veselov equations are solved by using this approach.     

The study of soliton fission and fusion in (2+1)-dimensional nonlinear system

By means of a variable separation approach and an extended homogeneous balance method, a general variable separation excitation of a (2+1)-dimensional nonlinear system is derived. Based on the derived solution with arbitrary functions, we reveal soliton fission and fusion phenomena in the (2+1)-dimensional soliton system.     

A Series of Variable Separation Solutions and New Soliton Structures of (2+1)-Dimensional Korteweg-de Vries Equation

Variable separation approach is introduced to solve the (2 1)-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model (24). Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately.     

New localized excitations and cross-like fractal structures to the (2+1)-dimensional Broer–Kaup system

A broad general variable separation solution with two arbitrary lower-dimensional functions of the (2+1)-dimensional Broer–Kaup (BK) equations was derived by means of a projective equation method and a variable separation hypothesis. Based on the derived variable separation excitation, some new special types of localized solutions such as oscillating solitons, instanton-like and cross-like fractal structures are revealed by selecting appropriate functions of the general variable separation solution.     

Baecklund Transformations for the Initial Problems of Nizhnich and Nizhnich－Novikov－Veselov Equations

The homogeneous balance method is a method for solving genera/partial differential equations (PDEs). In this paper we solve a kind of initial problems of the PDEs by using the special Baecklund transformations of the initial problem. The basic Fourier transformation method and some variable-separation skill are used as auxiliaries. Two initial problems of Nizlmich and the Nizlanich-Novikov-Veselov equations are solved by using this approach.     

(1+1)维耦合Ito系统的单值和多值局域激发模式

在(1 1)维非线性动力学系统,人们发现不同的局域激发模式分别存在于不同的非线性系统.可是最近的若干研究表明,在高维非线性动力学系统中,如果选取适当的边值条件或初始条件时,人们可以同时找到若干不同的局域激发模式,如:紧致子、峰孤子、呼吸子和折叠子等.本文的主要目的是寻找(1 1)维非线性耦合Ito系统中的不同的局域激发模式.首先,基于一个特殊的Painlev-éBacklund变换和线性变量分离方法,求得了该系统具有若干任意函数的变量分离严格解.然后,根据得到的变量分离严格解,通过选择严格解中的任意函数,引入恰当的单值分段连续函数和多值局域函数,成功找到了耦合Ito系统若干有实际物理意义的单值和多值局域激发模式,如:峰孤子,紧致子和多圈孤子等.     

Connections BetweenA utocorrelat ion Function and Double-Pulse Excitation spectra

Formulas are presented that describe the general connections between the autocorrelation functions and the double-pulse excitation probabilities. The formulas are derived using the time-dependen t perturbation theory and the rotating-wave approximation for the laser pulses. These formulas can be used to obtain the autocorrelation function from the doublepulse excitation probability or vice versa in many systems.