Discrete local induction equation

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

Discrete local induction equation

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

Department of Engineering and Design

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 nonlinear Schrödinger equation. In this paper, we present its discrete analogue, namely, a model of deformation of discrete space curves by the discrete nonlinear 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
Journal	Unknown Journal
Publication status	Published - 2017 Aug 4

ASJC Scopus subject areas

General

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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 nonlinear Schr{\"o}dinger equation. In this paper, we present its discrete analogue, namely, a model of deformation of discrete space curves by the discrete nonlinear 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 - 2017/8/4

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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 nonlinear Schrödinger equation. In this paper, we present its discrete analogue, namely, a model of deformation of discrete space curves by the discrete nonlinear 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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