Combined breathing-kink modes in the FPU lattice

Combined breather-kink modes have been observed in several systems. Here we show that in the FPU lattice, small amplitude breathing-kink modes are three-soliton solutions of an associated mKdV equation. Since this is integrable, the modes can be constructed using the Bäcklund transform. As well as finding explicit solutions, we consider the stability of the combined mode using variational techniques and illustrate stability for some parameter values and instability for others.     

Small amplitude limit of solitary waves for the Euler–Poisson system

The one-dimensional Euler–Poisson system arises in the study of phenomena of plasma such as plasma solitons, plasma sheaths, and double layers. When the system is rescaled by the Gardner–Morikawa transformation, the rescaled system is known to be formally approximated by the Korteweg–de Vries (KdV) equation. In light of this, we show existence of solitary wave solutions of the Euler–Poisson system in the stretched moving frame given by the transformation, and prove that they converge to the solitary wave solution of the associated KdV equation as the small amplitude parameter tends to zero. Our results assert that the formal expansion for the rescaled system is mathematically valid in the presence of solitary waves and justify Sagdeev's formal approximation for the solitary wave solutions of the pressureless Euler–Poisson system. Our work extends to the isothermal case.     

论《马氏文通》之同次

同次是一个独立于主、宾、正、偏四次,仿照拉丁文中的同位语,通过变换分析,针对语义指向而设立的一个术语。其目的不在于分析句法成分,而在于指明语义关系。     

Travelling wave solutions of some classes of nonlinear evolution equations in (1+1) and (2+1) dimensions

The tanh method is proposed to find travelling wave solutions in (1+1) and (2+1) dimensional wave equations. It can be extended to solve a whole family of modified Korteweg–de Vries type of equations, higher dimensional wave equations and nonlinear evolution equations.     

《世说新语》心理动词研究

本文将《世说新语》中的心理动词从心理学的角度分为情绪类心理动词、认知类心理动词和意志类心理动词,并对这三类心理动词进行了简要的分析。我们发现:情绪类心理动词在这三类心理动词中最多,占6812％;认知类心理动词较少,越高级的认知活动,其相应的动词越少;复音词有了一定的发展,但单音词在数量上和使用频率上仍占有优势。     

杨万里诗社与南宋孝宗朝政治

中国古代士人的官员身份,决定了他们的诗社往往与政治密不可分。杨万里一生多有结社,其社友多具有共同的政治倾向,并在孝宗年间论定高宗庙号、高庙配享二事上表现出了诗社的凝聚力和影响力。     

中国古代测量天体赤道坐标的方法

对中国古代测量天体赤道坐标的方法进行了探讨,其中包括明代科学家周述学等有关测量天体赤道坐标的重要新史料,并对元代赵友钦《革象新书》中的有关记载进行了研究和复原(绘制了复原图)。文中初步弄清了中国古代用仪器测量天体赤道坐标的方法。     

人格修养与中国画人艺术修养之嬗变——徐复观对中国绘画之心性学考察之三

徐复观对中国画人艺术修养之嬗变的心性学考察，论速了“外师造化，中得心源”到“一画”之间的精神升进关系，而这种升进正是画人人格修养工夫之所致。在此基础上，徐复观进一步提出“画的究竟义”。由此可以解明艺术在以心性学为主导的中国文化中的根本精神之所在。     

从《胡适留学日记》探析胡适早期的文化启蒙立场

胡适是二十世纪最有影响和最具声望的文化名人之一。文章通过对《胡适留学日记》的梳理和分析认为,胡适早期所形成的文化启蒙立场,可能是他之所以能“暴得大名”而“开风气”的原因所在。     

The two-dimensional transmission and reflection of a solitary wave

In the present paper, limited to the discussion of weak non-linear shallow water waves, the transmission and reflection of a planar soliton on a two-dimensional structure are considered. The whole flow field is divided mainly into two subfields. One is in the vicinity of the structure, called the inner field; the other is far from the structure, called the outer field. In the outer field, according to its definition, the influence of the structure on the flow is negligible; to the order O(α, β) the governing equation for the flow is replaced by the Boussinesq equation. In the inner field the effect of the structure on the flow is significant, so the full Laplace equation is adopted as the governing equation for the flow field. Then the matched asymptotic expansion method is employed to connect smoothly the inner and outer solutions. Owing to the irregularity of the bottom of the structure, the boundary element method is incorporated. As an example, the case in which the incoming wave is a solitary wave is calculated and the time histories of transmitted and reflected waves are plotted.