SU（N）上的微分几何：左不变向量场和右不变向量场及一元形式

$SU\left(M|N\right) $ Chern-Simons场论中的纽结

Knots in $SU\left(M|N\right) $ Chern-Simons Field Theory

研究了具有李超规范群$SU\left(M|N\right) $的Chern-Simons场论中的纽结，在$\mathfrak{su}\left(M|N\right) $的基本表象下得到了具有扭关系的$% S_{L}\left(α,β,z\right) $多项式不变量.

A short note on the appearance of the simplest antilinear ODE in several physical contexts

In this short note, we review several one-dimensional problems such as those involving linear Schroedinger equation, variable-coefficient Helmholtz equation, Zakharov-Shabat system and Kubelka-Munk equations. We show that they all can be reduced to solving one simple antilinear ordinary differential equation $u^{\prime}\left(x\right)=f\left(x\right)\overline{u\left(x\right)}$ or its nonhomogeneous version $u^{\prime}\left(x\right)=f\left(x\right)\overline{u\left(x\right)}+g\left(x\right)$, $x\in\left(0,x_{0}\right)\subset\mathbb{R}$. We point out some of the advantages of the proposed reformul…

反平方根势$V\left( r\right) =-\fracα{\sqrt{r}}$的精确解

Exact solution of inverse-square-root potential $V\left( r\right) =-\fracα{\sqrt{r}}$

本文给出了三维球对称反平方根势$V\left( r\right) =-\fracα{\sqrt{r}}$的精确解，包括散射和束缚态解。

关于二次Liénard型方程$\ddot{x}+f\left(x\right) \dot{x}^{2}+g\left( x\right) =0$的李点对称分类的观察[ JMP 54，053506（2013）]及其勘误[ JMP 55，059901（2014）]

An observation on Classification of Lie point symmetries for quadratic Liénard type equation $\ddot{x}+f\left(x\right) \dot{x}^{2}+g\left( x\right) =0$ [JMP 54, 053506 (2013)] and its erratum [JMP 55, 059901 (2014)]

我们证明了一个简化的一些最近的工作分类的李对称的Liénard型二次方程。我们认为，这个问题本来可以更简单地解决。

具有$U_{q}[\mathrm{osp}\left(2|2\right)^{\left(2\right)}]$对称性的十九顶点模型的反射$K$ -矩阵

Reflection $K$-matrices for a nineteen vertex model with $U_{q}[\mathrm{osp}\left(2|2\right)^{\left(2\right)}]$ symmetry

我们导出了由扭曲量子仿射李超代数$U_{q}[\mathrm{osp}\left(2|2\right)^{\left(2\right)}]\simeq U_{q}[C\left(2\right)^{\left(2\right)}]$的三维表示所构造的超对称十九顶点模型的边界Yang-Baxter方程的解.我们找到了三种解决方案。第一类解的特征在于三个边界自由参数和相应的反射$K$ -矩阵的所有元素都不为零。在II型解中，反射$K$ -矩阵是偶的（具有奇奇偶校验的$K$ -矩阵的每个元素为空）并且它仅具有一个边界自由参数。最后，III型解决方案对应于一个对角反射$K$ -矩阵与两个边界自由参数。

Right and left inverse scattering problems formulations for the Zakharov-Shabat system

We consider right and left formulations of the inverse scattering problem for the Zakharov-Shabat system and the corresponding integral Gelfand-Levitan-Marchenko equations. Both formulations are helpful for numerical solving of the inverse scattering problem, which we perform using the previously developed Toeplitz Inner Bordering (TIB) algorithm. First, we establish general relations between the right and left scattering coefficients. Here, along with the known results, we introduce a relation between the left and right norming coefficients for the N-soliton solution. Then we propose an auxil…