论文标题
R^n的几何通风曲线流
The Geometric Airy Curve Flow on R^n
论文作者
论文摘要
Langer和Perline证明，如果X是R^n的几何通风曲线流的解决方案，则在每个t上存在一个平行的正常框架，以使相应的主曲率满足（N-1）组件修改KDV（VMKDV_N）。他们还构建了高阶曲线流，其主曲线是VMKDV_N Soliton层次结构中高阶流量的解决方案。在本文中，我们在通过弧长参数的r^n曲线空间上写下了泊松结构，表明几何通风曲线流量是哈密顿式的，写下一系列通勤的汉密尔顿人，并构建了靠背转换和脱位索尼顿解决方案。
Langer and Perline proved that if x is a solution of the geometric Airy curve flow on R^n then there exists a parallel normal frame along x(. ,t) for each t such that the corresponding principal curvatures satisfy the (n-1) component modified KdV (vmKdV_n). They also constructed higher order curve flows whose principal curvatures are solutions of the higher order flows in the vmKdV_n soliton hierarchy. In this paper, we write down a Poisson structure on the space of curves in R^n parametrized by the arc-length, show that the geometric Airy curve flow is Hamiltonian, write down a sequence of commuting Hamiltonians, and construct Backlund transformations and explicit soliton solutions.
