论文标题
在双曲线空间中的常规螺旋多边形的Schrödinger图上
On the Schrödinger map for regular helical polygons in the hyperbolic space
论文作者
论文摘要
主要目的是描述$ \ xt = \ xs \ wedge_- \ xss的演变，带有$ \ x（s，0）$的$ $ \ x（s，0）$的常规多边形曲线，在3维超薄空间中具有非零扭转。与欧几里得空间不同，非零的扭转意味着两条不同的螺旋曲线。但是，De La Hoz，Kumar和Vega开发的最新技术帮助我们在理论上和数字上都在理性时代描述了进化，从而描述了相似性和差异。 数值实验表明，点$ \ x（0，t）$的轨迹表现出Riemann的非不同函数的新变体，其结构取决于问题中的初始扭转。结果，使用这些新的解决方案，表明双曲线空间中的平滑解决方案（螺旋，直线）显示出与其欧几里得对应物和曲线零扭转相同的不稳定性。这些数值观察与Banica和Vega获得的一些最新理论结果一致。
The main purpose is to describe the evolution of $\Xt = \Xs \wedge_- \Xss,$ with $\X(s,0)$ a regular polygonal curve with a nonzero torsion in the 3-dimensional hyperbolic space. Unlike in the Euclidean space, a nonzero torsion implies two different helical curves. However, recent techniques developed by de la Hoz, Kumar, and Vega help us in describing the evolution at rational times both theoretically and numerically, and thus, the similarities and differences. Numerical experiments show that the trajectory of the point $\X(0,t)$ exhibits new variants of Riemann's non-differentiable function whose structure depends on the initial torsion in the problem. As a result, with these new solutions, it is shown that the smooth solutions (helices, straight line) in the hyperbolic space show the same instability as displayed by their Euclidean counterparts and curves with zero-torsion. These numerical observations are in agreement with some recent theoretical results obtained by Banica and Vega.
