Discrete local induction equation
Discrete local induction equation
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离散局部归纳方程
DOI：
10.1093/integr/xyz003
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Nozomu Matsuura and Yasuhiro Ohta
中科院分区：
文献类型：
--
作者：
Sampei Hirose;Jun-ichi Inoguchi;Kenji Kajiwara;Nozomu Matsuura and Yasuhiro Ohta
局部诱导方程或空间曲线上的副法线流是一个众所周知的空间曲线变形模型，因为它描述了涡丝的动力学，而复曲率由非线性薛定谔方程控制。在本文中，我们提出了它的离散模拟，即离散的非线性薛定谔方程的离散空间曲线的变形模型。我们还提出了明确的公式，光滑和离散曲线的功能的两个组成部分的KP层次。博边科
The local induction equation, or the binormal flow on space curves is a well-known model of deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature is governed by the non-linear Schrödinger equation. In this article, we present its discrete analogue, namely, a model of deformation of discrete space curves by the discrete non-linear Schrödinger equation. We also present explicit formulas for both smooth and discrete curves in terms offunctions of the two-component KP hierarchy.Communicated by: Alexander I. Bobenko