Discrete Local Induction Equation
Exactly Solvable and Integrable Systems
2019-05-07 v2 Differential Geometry
Abstract
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 nonlinear Schr\"odinger equation. In this paper, we present its discrete analogue, namely, a model of deformation of discrete space curves by the discrete nonlinear Schr\"odinger equation. We also present explicit formulas for both smooth and discrete curves in terms of functions of the two-component KP hierarchy.
Keywords
Cite
@article{arxiv.1708.01704,
title = {Discrete Local Induction Equation},
author = {Sampei Hirose and Jun-ichi Inoguchi and Kenji Kajiwara and Nozomu Matsuura and Yasuhiro Ohta},
journal= {arXiv preprint arXiv:1708.01704},
year = {2019}
}
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38 pages