Fractal localized structures related to Jacobian elliptic functions in the higher-order Broer－Kaup system

This work reveals a novel phenomenon—that the localized coherent structures of a (2﹢1)﹣dimensional physical model possesses fractal behaviours. To clarify the interesting phenomenon, we take the (2﹢1)﹣dimensional higher-order Broer－Kaup system as a concrete example. Starting from a B?cklund transformation, we obtain a linear equation, and then a general solution of the system is derived. From this some special localized excitations with fractal behaviours are obtained by introducing some types of lower-dimensional fractal patterns that related to Jacobian elliptic functions.     

一族Liouville可积系及其约束流的Lax表示、Darboux变换

利用屠规彰格式求出了一族Liouville可积系,通过高阶位势特征函数约束将可积系分解成x部分和t_n部分可积Hamilton系统,求出了该系统的Lax表示及三类Darboux变换。     

Analytical Solution for Single—Mode Time—Dependent Oscillator

Based on the general theory of time-dependent quantum transformation,we use the “time evolution operator” method to solve the single-mode time-dependent oscillator.     

Solving Generalized Non-degenerate Two-Mode Two-Photon Jaynes-Cummings Model by Supersymmetric Unitary Transformation

Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transformation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes-Cummings models which include any forms of intensity-dependent coupling, field-dependent detuning, and field nonlinearity. Its eigenvalue, eigenstates, and time evolution of state vector are obtained.     

Hawking radiation of Weyl neutrinos in a rectilinearly non—uniformly accelerating Kinnersley black hole

The quantum thermal effect of Weyl neutrinos in a rectilinearly non-uniformly accelerating Kinnersley black hole is investigated using the generalized tortoise coordinate transformation.The equations that determine the location,the Hawking temperature of the event horizon and the thermal radiation spectrum of neutrinos are derived.Our results show that the location and the temperature of the event horizon depend not only on the time but also on the angle.     

一类级数的模变换公式

本文纠正了Apostol在文[1]中给出了一类级数的模变换公式,作为应用,我们得到了ζ（3）的一个估计。     

固氢金属化转变压力的理论计算

 利用简单金属的赝势理论方法计算了固氢的金属转变压力,并探讨了金属氢可能的晶体结构及力、热物性。计算结果表明,在绝对零度条件下,分子态固氢（HCP结构）向原子相金属氢（FCC结构）的转变压力p_t=465.95 GPa。     

应用BP神经网络识别内层表面细小缺陷的研究

内层表面细小凹坑的识别是超声无损评估的一个难点。本文利用人工神经网络对于信号的分类功能,建构和训练了一个BP神经网络,并用它对尺寸为1mm的圆锥形和半球形两种凹坑成功地进行了识别。研究表明,应用凹坑回波的DCT谱作为缺陷特片输入,可使BP神经网络的训练和缺陷识别既快捷又有效。     

Study of the peak effect phenomenon in single crystals of 2H-NbSe2

The weakly pinned single crystals of the hexagonal 2H-NbSe₂ compound have emerged as prototypes for determining and characterizing the phase boundaries of the possible order-disorder transformations in the vortex matter. We present here a status report based on the ac and dc magnetization measurements of the peak effect phenomenon in three crystals of 2H-NbSe₂, in which the critical current densities vary over two orders of magnitude. We sketch the generic vortex phase diagram of a weakly pinned superconductor, which also utilizes theoretical proposals. We also establish the connection between the metastability effects and pinning.     

A discrete KdV equation hierarchy: continuous limit,diverse exact solutions and their asymptotic state analysis

In this paper, a discrete KdV equation that is related to the famous continuous KdV equation is studied. First, an integrable discrete KdV hierarchy is constructed, from which several new discrete KdV equations are obtained. Second, we correspond the first several discrete equations of this hierarchy to the continuous KdV equation through the continuous limit. Third, the generalized (m, 2N − m)-fold Darboux transformation of the discrete KdV equation is established based on its known Lax pair. Finally, the diverse exact solutions including soliton solutions, rational solutions and mixed solutions on non-zero seed background are obtained by applying the resulting Darboux transformation, and their asymptotic states and physical properties such as amplitude, velocity, phase and energy are analyzed. At the same time, some soliton solutions are numerically simulated to show their dynamic behaviors. The properties and results obtained in this paper may be helpful to understand some physical phenomena described by KdV equations.