Higher order dispersive effects in regularized Boussinesq equation

In this paper, we consider the higher order Boussinesq (HBq) equation which models the bi-directional propagation of longitudinal waves in various continuous media. The equation contains the higher order effects of frequency dispersion. The present study is devoted to the numerical investigation of the HBq equation. For this aim a numerical scheme combining the Fourier pseudo-spectral method in space and a Runge–Kutta method in time is constructed. The convergence of semi-discrete scheme is proved in an appropriate Sobolev space. To investigate the higher order dispersive effects and nonlinear effects on the solutions of HBq equation, propagation of single solitary wave, head-on collision of solitary waves and blow-up solutions are considered.     

Vortex shedding around a near-wall circular cylinder induced by a solitary wave

This study developed a two-dimensional generalized vortex method to analyze the shedding of vortices and the hydrodynamic forces resulting from a solitary wave passing over a submerged circular cylinder placed near a flat seabed. Numerical results for validation are compared with other numerical and experimental results, and satisfactory agreement is found. A series of simulations were performed to study the effects of gap-to-diameter ratio and incident wave height on vorticity pattern as well as the forces exerted on the cylinder. The range of the heights of incident waves is from 0.3h to 0.7h, where h is the still water depth. The range of the gap-to-diameter ratios is from 0.1 to 0.8. The results indicate that the flow pattern and the pressure distribution change significantly because of the close proximity of the seabed where the vorticity flux on the seabed-side surface of the cylinder is suppressed. Placing the cylinder nearer the seabed increases the drag and the positive lift on the cylinder. When the gap-to-diameter ratio increases, the pattern of vortices changes because of the interaction between the main recirculation zone and the shear layers separated from the gap. The maxima of drag, lift and total force increase linearly with the height of the incident wave.     

Global attraction to solitary waves for Klein–Gordon equation with mean field interaction

We consider a U(1)$\mathbf{U}(1)$-invariant nonlinear Klein–Gordon equation in dimension n?1$n?1$, self-interacting via the mean field mechanism. We analyze the long-time asymptotics of finite energy solutions and prove that, under certain generic assumptions, each solution converges as t→±∞$t\to \pm \infty$ to the two-dimensional set of all “nonlinear eigenfunctions” of the form ?(x)e−iωt$?(x)e^{-i\omega t}$. This global attraction is caused by the nonlinear energy transfer from lower harmonics to the continuous spectrum and subsequent dispersive radiation.     

Three-dimensional vortices in Abelian gauge theories

In this paper we consider an Abelian Gauge Theory in R⁴${\mathbb{R}}^4$ equipped with the Minkowski metric. This theory leads to a system of equations, the Klein–Gordon–Maxwell equations, which provide models for the interaction between the electromagnetic field and matter. A three-dimensional vortex is a finite energy solution of these equations in which the magnetic field looks like the field created by a finite solenoid. Under suitable assumptions, we prove the existence of vortex solutions.     

Explicit exact solutions for the (2 + 1)-dimensional Konopelchenko–Dubrovsky equation

In this paper, we construct new explicit exact solutions for the coupled the (2 + 1)-dimensional Konopelchenko–Dubrovsky equation (KD equation) by using a improved mapping approach and variable separation method. By means of the method, new types of variable-separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) for the KD system are successfully obtained. The improved mapping approach and variable separation method can be applied to other higher-dimensional coupled nonlinear evolution equations.     

宋代文学比较研究的力作

《叶梦得与苏轼》一书以历史上多有争议的叶梦得与宋代文学史上的冠冕人物苏轼作为研究对象,通过诸多领域的对比分析,较为客观地展现了当时的政治文化生态,为宋代文学的比较研究作了有意义的尝试。     

论李实《蜀语》的方言研究

《蜀语》从实际语言出发,忠实记录了大量的明末蜀方言词语,包括形、音、义三方面的内容;考察了一部分蜀方言词语在辞书中的记载情况以及在文献中的使用情况,考证了一部分蜀方言本字并辨析了相关的文字字形。《蜀语》是研究明末蜀方言的重要资料,其断代断域的方言记载和研究模式对后代的方言研究产生了巨大的影响。     

西方文化与胡适文学思想之影响研究述评

目前对胡适文学思想与西方文化之间的影响研究,一是肯定了胡适与西方思想文化的关系,二是对白话诗与西方诗歌资源的关系讨论较多,但在具体范围和具体论题还没有深入,比如,新材料的发现,白话文运动、现实主义和自由主义文学思想、白话诗、文学批评等与西方的关系等还未深入翔实的比较研究。     

On the influence of material properties on the wave propagation in Mindlin-type microstructured solids

A mathematical model describing 1D wave propagation in Mindlin-type microstructured solids with nonlinearities in the macro- and microscale is used for studying propagation of solitary waves in such media. The results could be used for the stress analysis as well as for the nondestructive testing of material properties. The model equations are solved numerically under the localized initial conditions and periodic boundary conditions by the pseudospectral method. It is demonstrated how the values of the model parameters influence the wave propagation, the evolution and the interaction of waves under the framework of considered models. For this reason the solutions of the model equations are compared under different parameter combinations against one fixed combination of material parameters which is called ‘the reference case’.