On the preservation of invariants in the simulation of solitary waves in some nonlinear dispersive equations

In this paper we generalize some results in the literature concerning the structure of numerical approximations to solitary wave solutions of some nonlinear, dispersive equations is studied. We prove that those time discretizations with the property of preserving, exactly or approximately up to certain order, some invariants of the problems, have a better propagation of the error and provide a more suitable simulation of the solitary waves. The generalization involves the treatment of nonlocal operators and two different kinds of equations.     

胸中山水奇天下，删去临摹手一双--石涛与汪野亭山水画比较

以汪野亭的山水瓷画为对象，结合石涛的绘画作品及绘画理论，从汪野亭山水瓷画的构图、造型、笔墨三方面入手，探求石涛的山水创作对汪野亭的山水瓷画的影响，尤其是汪野亭作品中坚持石涛“搜尽奇峰打草稿”的创作理念和坚守“我为我法”的艺术追求。     

王存生平考--兼论王存与苏轼的交游

王存是润州人，是北宋重臣、著名地理学家，但对其展开的研究是不充分的，甚至有混淆视听的现象。对其生平进行梳理，有助于匡正视听；对其与苏轼的交往进行梳理，有助于对其政治取向有更清楚的了解。这些对于深入挖掘镇江的历史文化资源、拓展镇江的旅游资源都是有益的。     

Solitary waves for Non-Destructive Testing applications: Delayed nonlinear time reversal signal processing optimization

An original signal processing method called delayed Time Reversal-Nonlinear Elastic Wave Spectroscopy is introduced in the present paper. The method could be used to amplify signal in certain regions of the material under Non Destructive Testing. It allows to optimize and change the shape of the received focused wave in the material, either by making the focusing sharper by decreasing the side lobes or making it wider by modifying the actual focusing peak. It is also possible to use the focused signal as a delta-basis to construct a signal with arbitrary envelope or reduce the side lobes of the focused signal. These concepts are shown to work well in the simulations and the physical experiments. This signal processing method is particularly promising for nonlinear and solitary wave analysis, since it allows to create an interaction of sharp and solitary wave peaks just underneath the receiving transducer. Due to simple and accurate linear prediction of the received interaction signal, any differences of measurements and predictions could indicate the presence of nonlinearities.     

Generation of stable solitary waves by a piston-type wave maker

The focus of present study is on how to generate solitary waves as pure as possible by using a piston type wave maker. A meshless numerical model, which can simulate the trajectories of fluid particles in a wave motion exerted by the wave paddle, is established for the purpose of present study. The present numerical model is verified by the comparison with experimental data before it is employed to the focused problem. Various wave paddle motions are considered. The results show that solitary waves generated by applying Fenton’s solitary solution to the paddle motion proposed by Goring are purer than those generated by other paddle motions.     

Large-amplitude internal solitary waves in a two-fluid modelOndes solitaires internes de grande amplitude dans un modèle à deux fluides

We compute solitary wave solutions of a Hamiltonian model for large-amplitude long internal waves in a two-layer stratification. Computations are performed for values of the density and depth ratios close to oceanic conditions, and comparisons are made with solutions of both weakly and fully nonlinear models. It is shown that characteristic features of highly nonlinear solitary waves such as broadening are reproduced well by the present model. To cite this article: Ph. Guyenne, C. R. Mecanique 334 (2006).     

受迫耗散Boussinesq方程的可积性质和孤波解的探讨

考虑到耗散效应和地形外力,Rossby波的振幅可由受迫耗散Boussinesq方程来描述.当包含这两项时,模型比较复杂,不具有Painleve性质.通过将模型双线性化,双线性方法是一个可寻找孤波解和B(a|¨)cklund变换的方法.通过截断的Painleve展开式,得到了将方程双线性化的合适的因变量变换.然后得到了受迫耗散Boussinesq方程的单孤波解和B(a|¨)cklund变换.     

An extended Petviashvili method for the numerical generation of traveling and localized waves

A family of fixed-point iterations is proposed for the numerical computation of traveling waves and localized ground states. The methods are extended versions of Petviashvili type, and they are applicable when the nonlinear term of the system contains homogeneous functions of different degree. The methods are described and applied to several examples of interest, that calibrate their efficiency.     

论苏轼在密州的思想

苏轼知密州时期是其思想成熟的重要阶段。修建超然台、创作《超然台记》等标志着其超然思想初步形成;第一次为政一方,灭蝗、抗旱、上书申请减免赋税等明显地体现民本思想;具体施政中则施行了"贵清静而民自安"的黄老思想;其文学创作中的"超然诗"、出猎词等则体现了明显的爱国思想、归隐思想、野性思想等。