Low Dimensional Cohomology of Hom-Lie Algebras and q-deformed W（2, 2） Algebra

This paper aims to study low dimensional cohomology of Hom-Lie algebras and the qdeformed W(2, 2) algebra. We show that the q-deformed W(2, 2) algebra is a Hom-Lie algebra. Also,we establish a one-to-one correspondence between the equivalence classes of one-dimensional central extensions of a Hom-Lie algebra and its second cohomology group, leading us to determine the second cohomology group of the q-deformed W(2, 2) algebra. In addition, we generalize some results of derivations of finitely generated Lie algebras with values in graded modules to Hom-Lie algebras.As application, we compute all αk-derivations and in particular the first cohomology group of the q-deformed W(2, 2) algebra.     

Generalized dromions of the (2+1)-dimensional nonlinear Schrdinger equations

IntroductionMost of the mathematical work in the realm of nonlinear phenomena refers to integrablenonlinear equation and their exact soluted. The existence of more generalized locajized solutions for the (2+l)-dimensional KdV ~boil] and the (2+1)-dimensional breaking solitonequationl'] apart from the basic dro~ ~.sl3'41 has given an impetus to search for amore general class of localized sol~ in Oafs (2+1)-dimensional nonlinear evolution equations. Recelltlyt stating from the symmeq constraint…     

Matching Realization of Uq（sln＋1） of Higher Rank in the Quantum Weyl Algebra Wq（2n）

In the paper, we further realize the higher rank quantized universal enveloping algebra Uq（sln＋1） as certain quantum differential operators in the quantum Weyl algebra Wq （2n） defined over the quantum divided power algebra Sq（n） of rank n. We give the quantum differential operators realization for both the simple root vectors and the non-simple root vectors of Uq（sln＋1）. The nice behavior of the quantum root vectors formulas under the action of the Lusztig symmetries once again indicates that our realization model is naturally matched.     

The Cauchy Problem of the Nonlinear Schr■dinger Equations in R~(1 1)

In this paper,we consider the local and global solution for the nonlinear Schrdinger equationwith data in the homogeneous and nonhomogeneous Besov space and the scattering result for small data.Thetechniques to be used are adapted from the Strichartz type estimate,Kato's smoothing effect and the maximalfunction(in time)estimate for the free Schrdinger operator.     

二维非线性Schr(o)dinger方程的辛与多辛格式

对满足周期边界条件的二维非线性Schrödinger方程,运用中心差分对该方程进行空间离散, 得到一个有限维Hamilton系统,然后用隐式Euler中点格式进行时间离散得到其辛格式. 针对该方程的多辛形式, 运用有限体积法离散,得到一种直平行六面体上的中点型多辛格式. 用所构造的辛与多辛格式对二维非线性Schrödinger方程的平面波解和奇异解进行数值模拟,结果验证了所构 造格式的有效性. 最后, 根据计算结果,对两种格式进行了分析和比较.       

特征2上的Special代数S(3,1)的投射表示

本文研究了特征为2的代数闭域上Special代数S(3,1)的投射不可分解模.利用Nakano给出的BGG互反性,并通过研究不可约S(3,1)模限制为W(2,1)模的分解模式,给出了特征标高度htx≤0的所有投射不可分解模同构类的代表元和Cartan不变量.     

On the Blowup Phenomenon for N-coupled Focusing Schrdinger System in R~d(d≥3)

We study blow-up,global existence and ground state solutions for the N-coupled focusing nonlinear Schr¨odinger equations.Firstly,using the Nehari manifold approach and some variational techniques,the existence of ground state solutions to the equations(CNLS) is established.Secondly,under certain conditions,finite time blow-up phenomena of the solutions is derived.Finally,by introducing a refined version of compactness lemma,the L2concentration for the blow-up solutions is obtained.     

(3+1)-维耦合高阶非线性Schrdinger方程的光学多畸形波

本文研究带有高阶项、时间色散项和非线性系数项的复杂(3+1)-维高阶耦合非线性Schrdinger(3DHCNLSE)方程的精确解.首先,利用相似变换将非自治的方程转化为自治的耦合Hirota方程;其次,采用Darboux变换方法得到耦合Hirota方程带有任意常数的有理解;最后,给出变系数3DHCNLSE方程带有任意常数的1阶和2阶多畸形波解.本文获得的(3+1)-维(3D)多畸形波解可以用来描述深海动力学波和非线性光学纤维中出现的一些物理现象.     

广义Witt代数$W(2, 1)$的投射不可分解模和Cartan不变理

研究了特征为2的代数闭域上广义Witt代数$W(2,\mathbf{1})$的 投射不可分解模, 给出了特征标高度$ht\chi\leq 0$的所有投射不可分解模同构类的代表元和Cartan不变量. 并且进一步讨论了既约包络代数$u(W(2,\mathbf{1}),\chi)$ 的表示型.     

半线性Schr(o)dinger方程初值问题的H1-适定性

在RN(N≥2)中讨论一类具时间依赖系数的半线性Schr(o)dinger方程初值问题的H1-适定性.通过Strichartz估计和解的先验估计,得到了系数零点阶数λ与临界适定指数σ之间的关系,在一定条件下证明了该问题的H1-局部适定性和整体适定性.     

弱于H1空间的L2-临界非线性Schr(o)dinger方程的柯西问题

讨论Hs(Rn)(n≥1,1-ε＜s＜1)中L2-临界焦聚型非线性Schr(o)dinger方程的柯西问题,这里ε＞0是一个可以表出的很小的数.主要结论给出了在有限时间破裂解的L2集中现象.同时,作为推论,得到了小初值解的整体存在性.     

A new approach for solutions of the (2 + 1)-dimensional cubic nonlinear Schrödinger equation

A new method to solve the nonlinear evolution equations is presented, which combines the two kind methods – the tanh function method and symmetry group method. To demonstrate the method, we consider the (2 + 1)-dimensional cubic nonlinear Schrödinger (NLS) equation. As a result, some novel solitary solutions of the Schrödinger equation are obtained. And graphs of some solutions are displayed.