Discrete local induction equation. Issue 1 (9th June 2019)

• Record Type: Journal Article
• Authors: Hirose, Sampei; Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro
• Is Part Of: Journal of integrable systems. Volume 4:Issue 1(2019)
• Publication Date: 2019-06-09
• Subjects: local induction equation -- discrete non-linear Schrödinger equation -- two-component KP hierarchy; Mathematics -- Periodicals; 510
• DOI: 10.1093/integr/xyz003
• Languages: English
• ISSNs: 2058-5985

Abstract

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 $\tau$ functions of the two-component KP hierarchy. Communicated by: Alexander I. Bobenko