扰动Nizhnik-Novikov-Veselov系统分形孤子渐近解

文章研究了一类扰动Nizhnik-Novikov-Veselov非线性系统, 利用特殊的渐近方法得到了相应系统分形孤子渐近解. 关键词： 孤子 渐近解 扰动     

Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order

In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.     

约瑟夫森结中周期解及其稳定性的解析分析

针对交流激励下电阻-电容分路的约瑟夫森结,采用增量谐波平衡法推导了系统中周期解的解析表达式,并运用Floquet理论分析了周期解的稳定性.发现系统处于稳定周期状态的同时,还存在着丰富的不稳定周期解.通过计算Floquet乘数,得到了系统稳定周期解失稳时的临界参数值,并确定了系统发生的分岔类型,从理论上证明了系统随激励电流幅值的增加由倍周期分岔通向混沌.解析分析与数值计算结果具有很好的一致性. 关键词： 约瑟夫森结 增量谐波平衡法 周期解 分岔     

分子间费米共振增强二元溶液体系的受激拉曼散射研究

研究了液芯光纤内不同体积比的甲苯和间二甲苯二元混合溶液的受激拉曼散射.实验结果表明:在不同的体积比之下二元溶液的环呼吸振动模式1002 cm^-1,甲基的CH伸缩振动模式2920 cm^-1 以及芳香环CH对称伸缩振动模式3058 cm^-1的拉曼带同时产生受激拉曼辐射,并且2920 cm^-1 和 3058 cm^-1 拉曼带的一阶受激拉曼散射阈值要低于1002 cm^-1拉曼带的二阶 关键词： 分子间费米共振 二元溶液 受激拉曼散射 拉曼散射截面     

sine-Gordon型方程的无穷序列新精确解

为了获得sine-Gordon型方程的无穷序列精确解,给出三角函数型辅助方程和双曲函数型辅助方程及其Bäcklund变换和解的非线性叠加公式,借助符号计算系统Mathematica,构造了sine-Gordon方程、mKdV-sine-Gordon方程、(n+1)维双sine-Gordon方程和sinh-Gordon方程的无穷序列新精确解.其中包括无穷序列三角函数解、无穷序列双曲函数解、无穷序列Jacobi椭圆函数解和无穷序列复合型解. 关键词： sine-Gordon型方程 解的非线性叠加公式 辅助方程 无穷序列精确解     

远场模型方程的同伦近似对称约化

以同伦近似对称法为理论依据研究了远场模型方程, 通过归纳各阶相似约化解和各阶相似约化方程的通式构造相应的同伦级数解. 各阶相似约化方程均为线性变系数常微分方程, 并且可以从零阶开始依次求解. 同伦模型中的辅助参数影响同伦级数解的收敛性. 关键词： 同伦近似对称法 远场模型方程 同伦级数解     

一类相对转动非线性动力学模型的近似解

研究了一类具有非线性阻尼力和强迫周期力项的相对转动非线性动力学模型. 首先构造一个同伦映射, 其次决定方程的初始近似, 最后通过同伦映射方法得到了对应模型的任意次近似解. 关键词： 相对转动 非线性动力系统 近似解     

Relaxor behavior in the (1−x)BaSnO3 - xPbTiO3 solid solution

The relaxor behavior was revealed in the solid solution (1−x)BaSnO₃-xPbTiO₃[(1−x)BSn-xPT] with compositions near x=0.50. The real permittivity (ε^′) and loss tangent (tanδ) exhibit diffuse and dispersive maxima, whose temperature shifts towards a higher temperature upon the increasing frequency. The frequency dependence of the temperature of the dielectric maximum (T_m) follows the Vogel-Fulcher law, as in the canonical relaxor. A deviation from the Curie-Weiss law was observed below the Burns temperature (T_B) and well above the Curie temperature (T_C). These phenomena are well consistent with typical relaxors, which explains the existence of the relaxor behavior in the (1−x)BSn-xPT solid solution.     

Molar concentration-depth profiles at the solution surface of a cationic surfactant reconstructed with angle resolved X-ray photoelectron spectroscopy

In the current work, we first reconstructed the molar fraction-depth profiles of cation and anion near the surface of tetrabutylammonium iodide dissolved in formamide by a refined calculation procedure, based on angle resolved X-ray photoelectron spectroscopy experiments. In this calculation procedure, both the transmission functions of the core levels and the inelastic mean free paths of the photoelectrons have been taken into account. We have evaluated the partial molar volumes of surfactant and solvent by the densities of such solutions with different bulk concentrations. With those partial molar volumes, the molar concentration-depth profiles of tetrabutylammonium ion and iodide ion were determined. The surface excesses of both surfactant ions were then achieved directly by integrating these depth profiles. The anionic molar concentration-depth profiles and surface excesses have been compared with their counterparts determined by neutral impact ion scattering spectroscopy. The comparisons exhibit good agreements. Being capable of determining molar concentration-depth profiles of surfactant ions by core levels with different kinetic energies may extend the applicable range of ARXPS in investigating solution surfaces.     

From crystal steps to continuum laws: Behavior near large facets in one dimension

The passage from discrete schemes for surface line defects (steps) to nonlinear macroscopic laws for crystals is studied via formal asymptotics in one space dimension. Our goal is to illustrate by explicit computations the emergence from step motion laws of continuum-scale power series expansions for the slope near the edges of large, flat surface regions (facets). We consider surface diffusion kinetics via the Burton, Cabrera and Frank (BCF) model by which adsorbed atoms diffuse on terraces and attach-detach at steps. Nearest-neighbor step interactions are included. The setting is a monotone train of N steps separating two semi-infinite facets at fixed heights. We show how boundary conditions for the continuum slope and flux, and expansions in the height variable near facets, may emerge from the algebraic structure of discrete schemes as N→∞. Our technique relies on the use of self-similar discrete slopes, conversion of discrete schemes to sum equations, and their reduction to nonlinear integral equations for the continuum-scale slope. Approximate solutions to the continuum equations near facet edges are constructed formally by direct iterations. For elastic-dipole and multipole step interactions, the continuum slope is found in agreement with a previous hypothesis of ‘local equilibrium’.