Discrete Local Induction Equation

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

Research output: Contribution to journalArticlepeer-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 languageEnglish
Article numberxyz003
JournalJournal of Integrable Systems
Volume4
Issue number1
DOIs
Publication statusPublished - Jun 9 2019

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