Discrete Local Induction Equation

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

Research output: Contribution to journalArticle

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

    Fingerprint

Cite this

Hirose, S., Inoguchi, J. I., Kajiwara, K., Matsuura, N., & Ohta, Y. (2019). Discrete Local Induction Equation. Journal of Integrable Systems, 4(1), [xyz003]. https://doi.org/10.1093/integr/xyz003