Discrete Local Induction Equation

Sampei Hirose; Jun ichi Inoguchi; Kenji Kajiwara; Nozomu Matsuura; Yasuhiro Ohta

doi:10.1093/integr/xyz003

Discrete Local Induction Equation

Sampei Hirose, Jun ichi Inoguchi, Kenji Kajiwara, Nozomu Matsuura, Yasuhiro Ohta

Division of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

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 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 of τ functions of the two-component KP hierarchy.

Original language	English
Article number	xyz003
Journal	Journal of Integrable Systems
Volume	4
Issue number	1
DOIs	https://doi.org/10.1093/integr/xyz003
Publication status	Published - Jun 9 2019

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10.1093/integr/xyz003

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title = "Discrete Local Induction Equation",

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 non-linear Schr{\"o}dinger equation. In this article, we present its discrete analogue, namely, a model of deformation of discrete space curves by the discrete non-linear Schr{\"o}dinger equation. We also present explicit formulas for both smooth and discrete curves in terms of τ functions of the two-component KP hierarchy.",

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AU - Hirose, Sampei

AU - Inoguchi, Jun ichi

AU - Kajiwara, Kenji

AU - Matsuura, Nozomu

AU - Ohta, Yasuhiro

PY - 2019/6/9

Y1 - 2019/6/9

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AB - 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 of τ functions of the two-component KP hierarchy.

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DO - 10.1093/integr/xyz003

M3 - Article

SN - 2058-5985

VL - 4

JO - Journal of Integrable Systems

JF - Journal of Integrable Systems

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Discrete Local Induction Equation

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