一族新的Painleve可积的Burgers方程

寻找可积模型是非线性物理中的重要问题之一,Burgers方程和KkV方程是两个最重要的1＋1维可积模型,最近得到了两族新kdV型方程的可积推广,将Burgers方程作了类似的推广,并证明其中一族是Painleve 可积的。     

一族新的Painlev可积的Burgers方程

寻找可积模型是非线性物理中的重要问题之一．Ｂｕｒｇｅｒｓ方程和ＫｄＶ方程是两个最 重要的１＋１维可积模型．最近得到了两族新的ＫｄＶ型方程的可积推广将Ｂｕｒｇｅｒｓ方程作 了类似的推广,并证明其中一族是Ｐａｉｎｌｅｖｅ可积的．     

扰动非线性薛定谔方程的Painleve分析和精确孤立子解

指出扰动的非线性项仅在扰动项为零时,才具有Painleve性质．利用截断的Painleve分析方法得到了扰动非线性薛定谔方程的Backlund变换和5种形式的精确孤立子解．     

Formation of Vegetation Patterns and Hysteresis Phenomena in Arid and Semiarid Zones

Considering the spatial effect of the complicated interactions between plant and resource （soil water） and the stochastic character of the complicated ecological processes in an ecosystem, we introduce a lattice gas model to investigate the vegetation pattern formation in the arid and the semiarid ecosystems with Monte Carlo sim- ulations. With consistency of some previous mean-field models, the model reproduces a wide range of patterns observed in the arid and the semiarid regions. The sequences of vegetation states are also investigated with scanning three parameters, i.e., the precipitation and the plant growth rate, and then the parameter ranges are identified where a hysteresis loop appears and two different stable states coexist. The simulation results denote that the complex structures occur only when the precipitation parameter decreases. Moreover, based on the model, it is found that an increase of the competition of the plant for the resource along the slope direction results in the regular stripes parallel to the hill＇s contours. The model provides an interesting mechanism to understand the formation of the other regular vegetation stripe in a limited resource condition.     

Phase Transition of the Pair Contact Process Model in a Fragmented Network

We investigate the phase transition of the pair contact process （PCP） model in a fragmented network. The network is formed by rewiring the link between two nearest neighbors to another randomly selected site in one dimension with a probability q. When the average degree （k〉 = 2, the system exhibits a structure transition and the lattice is fragmented into several isolated subgraphs, it is shown that a giant cluster appears and its node fraction does not change nearly for q 〉 0. Furthermore, it is found that the critical behavior of the continuous phase transition for the PCP model is different from the directed percolation （DP） class and the estimated values of the critical exponents are independent of the rewiring probability for q 〉 0. We conjecture that the structure transition for （k） = 2 takes an important role in the change of the critical behavior of the continuous phase transition.     

K(m,n)方程的对称性约化

利用对称性约化的直接法,给出了具有非线性色散情况下的K(m,n)模型的所有对称性约化.从第一种约化方程的Painlev啨性质分析可知,K(m,n)模型仅当m=n+1和m=n+2时是可积的.特殊情况下(行波约化),这种约化的解可用一个积分表示.给出了K(m,1)和K(m,m)的一般孤波解的明显表达式. 关键词：