General Higher-Order Breather and Hybrid Solutions of the Fokas System

Fokas system is the simplest (2+1)-dimensional extension of the nonlinear Schr?dinger (NLS) equation (Eq.(2), Inverse Problems 10 (1994) L19-L22).By appropriately limiting on soliton solutions generated by the Hirota bilinear method, the explicit forms of $n$-th breathers and semi-rational solutions for the Fokas system are derived. The obtained first-order breather exhibits arange of interesting dynamics. For high-order breather, it has more rich dynamical behaviors.The first-order and the second-order breather solutions are given graphically. Using the long wave limit in soliton solutions, rational solutions are obtained, which are used to analyze the mechanism of the rogue wave and lump respectively.By taking a long waves limit of a part of exponential functions in $f$ and $g$ appeared in the bilinear form of the Fokas system, many interesting hybrid solutions are constructed. The hybrid solutions illustrate various superposed wave structures involving rogue waves, lumps, solitons, and periodic line waves. Their rather complicated dynamics are revealed.     

Fractional dynamics of coupled oscillators with long-range interaction

We consider a one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction. The corresponding term in dynamical equations is proportional to 1//n-m/alpha+1. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order alpha, when 0相似文献   

Lump waves,solitary waves and interaction phenomena to the (2 + 1)-dimensional Konopelchenko–Dubrovsky equation

In this paper, we investigated the $(2+1)$-dimensional Konopelchenko–Dubrovsky equation. The lump waves, solitary waves as well as interaction between lump waves and solitary waves are presented based on the Hirota bilinear form of this equation. It is worth noting that the rational solutions are obtained by taking a long wave limit, and we also discussed the lump solutions and rogue wave solutions. Moreover, all these solutions are presented via 3-dimensional plots and density plots with choosing some special parameters to show the dynamic graphs.     

Resonance Y-type soliton solutions and some new types of hybrid solutions in the(2+1)-dimensional Sawada–Kotera equation

In this paper, based on N-soliton solutions, we introduce a new constraint among parameters to find the resonance Y-type soliton solutions in (2+1)-dimensional integrable systems. Then, we take the (2+1)-dimensional Sawada–Kotera equation as an example to illustrate how to generate these resonance Y-type soliton solutions with this new constraint. Next, by the long wave limit method, velocity resonance and module resonance, we can obtain some new types of hybrid solutions of resonance Y-type solitons with line waves, breather waves, high-order lump waves respectively. Finally, we also study the dynamics of these interaction solutions and indicate mathematically that these interactions are elastic.     

First order phase transition from free flow to synchronized flow in a cellular automata model

This paper presents an improved cellular automata model, which is based on three phase traffic theory and can reproduce the first order phase transition from free flow to synchronized flow. The fundamental diagram, the spacetime plots, and the 1-min average flux density diagram are presented. The autocorrelation and cross correlation functions are studied to identity the synchronized flow state. It is shown that the results of the model are well consistent with the empirical findings.     

High-Order Lump-Type Solutions and Their Interaction Solutions to a (3+1)-Dimensional Nonlinear Evolution Equation *

By means of the Hirota bilinear method and symbolic computation, high-order lump-type solutions and a kind of interaction solutions are presented for a (3+1)-dimensional nonlinear evolution equation. The high-order lump-type solutions of the associated Hirota bilinear equation are presented, which is a kind of positive quartic-quadratic-function solution. At the same time, the interaction solutions can also be obtained, which are linear combination solutions of quartic-quadratic-functions and hyperbolic cosine functions. Physical properties and dynamical structures of two classes of the presented solutions are demonstrated in detail by their graphs.      

Soliton-Like Solutions for the (2+1)-Dimensional High-Order Broer-Kaup Equations

By using the extended homogeneous balance method,we give new soliton-like solutions for the (2 1)-dimensional high-order Broer-Kaup equations.Solitary wave solutions are shown to be a special case of the present results.     

Degree of fourth-order coherence by double Hanbury Brownben Twiss detections

Photon quantum statistics of light can be shown by the high-order coherence. The fourth-order coherences of various quantum states including Fock states, coherent states, thermal states and squeezed vacuum states are investigated based on a double Hanbury Brown–Twiss (HBT) scheme. The analytical results are obtained by taking the overall efficiency and background into account.     

Difference equations for N-solitons solutions to KdV

Using a newly-developed method, it is shown that the N-soliton solutions to the Korteweg-de Vries equation satisfy high-order difference equations in the spectral parameter. These equations are exhibited explicitly.     

Construction of low dissipative high-order well-balanced filter schemes for non-equilibrium flows

The goal of this paper is to generalize the well-balanced approach for non-equilibrium flow studied by Wang et al. (2009) [29] to a class of low dissipative high-order shock-capturing filter schemes and to explore more advantages of well-balanced schemes in reacting flows. More general 1D and 2D reacting flow models and new examples of shock turbulence interactions are provided to demonstrate the advantage of well-balanced schemes. The class of filter schemes developed by Yee et al. (1999) [33], Sjögreen and Yee (2004) [27] and Yee and Sjögreen (2007) [38] consist of two steps, a full time step of spatially high-order non-dissipative base scheme and an adaptive non-linear filter containing shock-capturing dissipation. A good property of the filter scheme is that the base scheme and the filter are stand-alone modules in designing. Therefore, the idea of designing a well-balanced filter scheme is straightforward, i.e. choosing a well-balanced base scheme with a well-balanced filter (both with high-order accuracy). A typical class of these schemes shown in this paper is the high-order central difference schemes/predictor–corrector (PC) schemes with a high-order well-balanced WENO filter. The new filter scheme with the well-balanced property will gather the features of both filter methods and well-balanced properties: it can preserve certain steady-state solutions exactly; it is able to capture small perturbations, e.g. turbulence fluctuations; and it adaptively controls numerical dissipation. Thus it shows high accuracy, efficiency and stability in shock/turbulence interactions. Numerical examples containing 1D and 2D smooth problems, 1D stationary contact discontinuity problem and 1D turbulence/shock interactions are included to verify the improved accuracy, in addition to the well-balanced behavior.     

各向异性海森伯自旋链中的超椭圆函数波解

在霍尔斯坦-普里马科夫表象中研究了各向异性海森伯自旋链模型.在半经典近似条件下,考虑高阶非线性项和周期性边界条件,应用相干态求出了用雅可比椭圆函数的反函数的组合表示的超椭圆函数波解,并讨论了解的物理意义.     

高精度格式WCNS-E-5计算物面热流

采用加权紧致非线性格式WCNS-E-5,四阶精度的二阶导数差分近似以及四阶精度的边界格式构造了高精度算法,对高超声速粘性流动的物面热流进行数值研究.首先考察了壁面网格雷诺数对驻点热流的影响,然后开展了边界格式对热流计算结果影响的研究,最后对大攻角钝锥绕流进行了数值模拟.研究结果表明:WCNS-E-5能降低边界层内网格分辨率,全场高精度的WCNS-E-5计算得到的流场图像清晰、真实、分辨率高,热流值准确、可靠.     

Numerical simulation of propagation of a femtosecond optical soliton in a single-mode fiber with allowance for the imaginary part of Raman response

We consider the effect of Raman inertial response of a medium on the stability of a first-order femtosecond soliton. Numerical solution to the high-order nonlinear Schrödinger equation, with the complex Raman term, describing propagation of a femtosecond optical soliton in a single-mode fiber, is obtained. It is shown that a soliton solution of the high-order nonlinear Schrödinger equation exists under certain conditions imposed on the equation coefficients. These conditions lead to limitations on the wavelength, fiber type, and the highest energy. Results of numerical solutions are in agreement with available experimental data.     

Statistical entropies of extremal Kaluza-Klein AdS black holes in arbitrary dimensions

We have investigated the microscopic interpretations of the entropies for the four-dimensional extremal Kaluza-Klein AdS black hole and its higher-dimensional generalizations by using the Kerr/CFT correspondence. These newly-found Kaluza-Klein AdS black holes are charged rotating asymptotically AdS black hole solutions of gauged supergravity in four and higher dimensions. With suitable boundary conditions on the perturbations of the near-horizon geometry, it is shown that the asymptotic symmetry generators form a two-dimensional Virasoro algebra with a central term. By utilizing the central charge and the temperature of the dual conformal field theory, Cardy formula reproduces the expected Bekenstein-Hawking entropy. Directly working on the ordinary metrics of the extremal Kaluza-klein AdS black holes without taking the near-horizon limit, we also re-derive their microscopic entropies.     

A Parameter-Free Generalized Moment Limiter for High-Order Methods on Unstructured Grids

A parameter-free limiting technique is developed for high-order unstruc- tured-grid methods to capture discontinuities when solving hyperbolic conservation laws. The technique is based on a "troubled-cell" approach, in which cells requiring limiting are first marked, and then a limiter is applied to these marked cells. A parameter-free accuracy-preserving TVD marker based on the cell-averaged solutions and solution derivatives in a local stencil is compared to several other markers in the literature in identifying "troubled cells". This marker is shown to be reliable and efficient to consistently mark the discontinuities. Then a compact high-order hierarchical moment limiter is developed for arbitrary unstructured grids. The limiter preserves a degree $p$ polynomial on an arbitrary mesh. As a result, the solution accuracy near smooth local extrema is preserved. Numerical results for the high-order spectral difference methods are provided to illustrate the accuracy, effectiveness, and robustness of the present limiting technique.     

各向异性介质三维电磁响应模拟的Ho-GEBA算法

本文基于积分方程法研究并建立了一种模拟横向同性介质中任意各向异性异常 体三维电磁响应的高阶广义扩展Born近似(Ho-GEBA)算法. 首先利用逐次迭代技术给出积分方程的广义级数展开解, 为保证其收敛性, 引入一种各向异性条件下满足压缩映射的迭代算子. 然后利用异常体区域分解技术, 并结合扩展Born近似原理, 得到各向异性介质三维电磁响应的Ho-GEBA解. 为提高效率, 计算过程中采用并矢Green函数的解析表达式. 最后通过数值计算实例对比验证了本文算法的有效性. 关键词： 高阶广义扩展Born近似 积分方程 电磁模拟 解析Green函数     

Dependence of the integral polariton effect on the crystal thickness and light incidence geometry

Solutions of the problems of integrated absorption and amplitude-phase dispersion relations for transmission spectra in the range of isolated exciton resonances taking into account the interference of exciton-polariton waves based on the application of the causality principle to optical response functions and the limiting transition of these solutions for thick crystals are considered. It is shown that the results obtained are equivalent in the limit to the results of single-wave solution, which considers a wave with the least absorption. Generalization to the case of oblique incidence of light is performed.     

W∞ Algebra and High-Order Virasoro Algebra

We give the relation between W_∞ algebra and high-order Virasoro algebra (HOVA), i.e., W_∞ algebra is the limit of HOVA. Then we give the super high-order Virasoro algebra from super W_∞ algebra.     

Collective behaviors in coupled map lattices with local and nonlocal connections

After having recalled the basic properties of the nontrivial collective dynamics exhibited by lattices of maps with local coupling and synchronous updating, we present the behavior of the same models in which all the connections are random. The mean-field, synchronized limit is shown to be reached only for large enough connectivities and sufficiently strong local chaos. Intermediate models, in which only a few of the connections of each site are taken at random, are then considered. Preliminary results indicate that the nontrivial collective behaviors shown by the regularly connected models may be robust to a small proportion of nonlocal, random connections.