Analysis to Some Solutions Obtained by Modified Extended tanh-Function Method＊

First, two tanh-coth type solutions of a class of nonlinear wave equation are derived by using a simplified modified extended tanh-function method. Then, further analysis to some tanh-coth type solutions of nonlinear evolution equations are given. The results show that when balance number m is one or two, the tanh-eoth type solutions obtained by the modified extended tanh-funetion method can be obtained by using the hyperbolic-function method.     

弹性矩形板方程在非线性边界条件下整体解的存在唯一性

考虑了在非线性边界条件下的弹性矩形板方程.利用Galerkin方法,首先证明了该方程在非线性边界(a)及初值w⁰∈W,w¹∈W的条件下初边值问题存在唯一整体弱解w(t).其次证明了该方程在非线性边界(b)及初值w⁰∈W₁,w¹∈W₁的条件 关键词： 弹性矩形板方程 非线性边界条件 初边值问题 整体解     

New solitary wave solutions for nonlinear evolution equations

Three important nonlinear evolution equations are solved with the aid of the symbolic manipulation system.Maple,using the direct algebraic method proposed recently,We explicitly obtain several new solutions of physical interest in addition to rederiving all the known solutions.     

Effects of co-substitution on the electrical properties of BiFeO3 thin films prepared by chemical solution deposition

Ferroelectric BiFeO₃ thin films with Nd-Cr (or Sm-Cr) co-substitution (denoted by BNdFCr and BSmFCr, respectively) were deposited on the Pt(2 0 0)/TiO₂/SiO₂/Si(1 0 0) substrates by a chemical solution deposition method. X-ray diffraction patterns revealed the formation of BNdFCr and BSmFCr thin films without any secondary phases. The co-substituted BNdFCr (or BSmFCr) thin films, which were annealed at 550 °C for 30 min in N₂ atmosphere, exhibited enhanced electrical properties compared to BFO thin films with the remanent polarization (2P_r) and coercive electric field (2E_c) of 196, 188 μC/cm² and 600, 570 kV/cm with the electric field of 800 kV/cm, respectively. The leakage current densities of BNdFCr and BSmFCr thin films measured at room temperature were approximately three orders of magnitude lower than that of BFO thin film, and the leakage current at room temperature of the thin films exhibited three distinctive conduction behaviors. Furthermore, the values of pulse polarizations [i.e., +(P*-P^{^}) or −(P*-P^{^})] of BNdFCr and BSmFCr thin films were reasonably unchanged up to 1.4 × 10¹⁰ switching cycles.     

荧光层析法研究由胶束溶液分离出的两种抗菌素

喹诺酮药物是一类重要的化学合成抗菌素 ,其临床应用正在不断扩大[1] 。氧氟沙星 (OFLX)和环丙沙星 (CPLX)结构非常相似。本文采用胶束薄层色谱法分离了两种药物。加入 1%氨水的 0 0 0 15mol·L-1十六烷基三甲基溴化铵 (CTAB)和 1%十二烷基磺酸钠 (SDS)的等体积水溶液作为展开剂 ,聚酰胺薄膜作为固定相。考查了CTAB浓度 ,SDS浓度及氨水对氧氟沙星和环丙沙星Rf 值的影响。在选定条件下 ,Rf 值分别为 0 87和 0 76 ,在激发波长为 2 80nm处对其进行了荧光测定。测定了该方法的稳定性和灵敏度。本文首次使用胶束溶液分离了氧氟沙星和环丙沙星     

Solving (2+1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method

By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2+1)-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the (2+1)-dimensional sine-Poisson equation are derived in a simple manner by this technique.     

Multiple bright and dark soliton solutions in three component spinor Bose-Einstein condensates

We investigate a quasi one dimensional spin-1 Bose-Einstein Condensates (BEC) in the absence of an external confinement governed by a system of three coupled Gross-Pitaevskii (GP) equation. Based on the Lax-pair, we construct one soliton solution employing gauge transformation method. In addition, the multiple bright and dark soliton solutions are obtained by properly choosing amplitude dependent parameter in the Lax-pair. The results of the paper emphasizes the richness in the structure of soliton solutions admitted by the spin components, a phenomenon which has never been brought out to the fore. We have also extended the gauge transformation method to generate two soliton solutions.     

Lump and interaction solutions to the (3+1)-dimensional Burgers equation

The(3+1)-dimensional Burgers equation, which describes nonlinear waves in turbulence and the interface dynamics,is considered. Two types of semi-rational solutions, namely, the lump–kink solution and the lump–two kinks solution, are constructed from the quadratic function ansatz. Some interesting features of interactions between lumps and other solitons are revealed analytically and shown graphically, such as fusion and fission processes.     

A modified NaSch model with density-dependent randomization for traffic flow

Based on the Nagel-Schreckenberg (NaSch) model of traffic flow, a modified cellular automaton (CA) traffic model with the density-dependent randomization (abbreviated as the DDR model) is proposed to simulate traffic flow. The fundamental diagram obtained by simulation shows the ability of this modified NaSch model to capture the essential features of traffic flow, e.g., synchronized flow, metastable state, hysteresis and phase separation at higher densities. Comparisons are made between this DDR model and the NaSch model, also between this DDR model and the VDR model. And the underlying mechanism is analyzed. All these results indicate that the presented model is reasonable and more realistic.     

一类大气浅水波方程的近似解

研究了一类非线性浅水波方程，利用同论映射理论和方法，得到了相应系统的近似解. 关键词： 浅水波 非线性 同伦映射 近似解