广义Camassa-Holm方程的行波解

运用平面动力系统理论和方法给出了广义Camassa-Holm方程在各种参数条件下的相图与分支,分析了奇线对其行波解的影响,获得了广义Camassa-Holm方程光滑、非光滑孤立波解和周期波解的存在性及个数,求出了它的两组新周期尖波解的显式表达式.     

含频散项的K(2,3)方程的精确行波解

本文研究了包含频散项的K(2,3)方程u_t+(u²)_x-(u³)_xxx=0的分支问题.利用动力系统的定性分析,并且借助Maple软件进行数值模拟得到行波解系统相应的相图,然后通过积分计算得到周期尖波解、类扭波和类反扭波的精确解的函数表达式,以及孤立波精确解的隐函数表达式.     

广义的WBK型耗散方程行波解的定性分析

运用平面动力系统理论对广义的WBK型耗散方程所对应的动力系统作了定性分析,给出了其在不同参数条件下的全局相图.研究了方程行波解的性态与耗散系数r之间的关系.     

弱耦合一维扩展赫伯特模型的基态相图

我们利用玻色化和重整化群分析的方法研究了半满填空且排斥势小于跃迁动能时的一维扩展赫伯特模型的基态相图,发现基态相图是由自旋密度波,电荷密度波和键荷密度波组成.这些结果揭示了扩展赫伯特模型和赫伯特模型基态相图的差异.     

小展弦比波的Green-Naghdi渐进模型的行波解（英文）

本文研究了小展弦比波的Green-Naghdi渐进模型.利用平面自治系统的稳定性分析方法,在不同的参数条件下,讨论了它的行波系统的分岔并且给出了对应的相图,得到了光滑周期波解,广义扭波解,广义反扭波解,广义紧波解,周期尖波解,孤波解和孤立尖波解的精确表达式.进一步,通过数学软件Maple模拟了这些解.     

Extended Bose-Hubbard model with pair hopping on triangular lattice

We study systematically an extended Bose-Hubbard model on the triangular lattice by means of a meanfield method based on the Gutzwiller ansatz. Pair hopping terms are explicitly included and a three-body constraint is applied. The zero-temperature phase diagram and a variety of quantum phase transitions are investigated in great detail. In particular, we show the existence and the stability of the pair supersolid phase.     

Effect of the Coadsorption of CO and O2 on the Phase Diagram of the Ziff—Gulari—Barshad Model

The effect of the coadsorption of CO and O2 on the Ziff-Gulari-Barshad surface catalytic reaction system in studied by Monte Carlo simulation.The coadsorption of both species adds an extra reaction step to the classical Ziff-Gulari-Barshad model.It is shown that the second-order phase transition from the reactive state to the O-passivated state in the Ziff-Gulari-Barshad model is eliminated,and the production rate of CO2 increases linearly along the fraction yco of CO in gas phase when it is low,in agreement with experimental results.We also find that the increase of the probability of the coadsorption leads to the decrease of the critical value of yco of the discontinuous phase transition to the CO-passivated state.     

格点定模SU(2)-Higgs模型的解析计算

对格点上基础表示的定模Higgs场与SU(2)规范场耦合系统的相图进行解析计算至累积展开的第四级,用扫瞄确定变分参数的方法,得到与Monte Carlo模拟很好符合的相图.计算了N_τ=1的有限温度情形下SU(2)-Higgs系统和纯SU(2)模型的Polyakov线,对后者得到迄今最佳的近似解析结果β_c.