Explicit formulas for isoperimetric deformations of smooth and discrete elasticae

• Shigetomi Shota

  Graduate School of Mathematics, Kyushu University

• Kajiwara Kenji

  Institute of Mathematics for Industry, Kyushu University

Abstract

We construct the explicit formula for the isoperimetric deformation of elastica described by the modified KdV equation. We also construct the explicit formulas for the continuous and discrete deformations of the discrete analogue of elastica described by the semi-discrete potential modified KdV equation and the discrete potential modified KdV equation, respectively. The formulas are given in terms of the elliptic theta functions.

Journal

• JSIAM Letters

  JSIAM Letters 13 (0), 80-83, 2021

  The Japan Society for Industrial and Applied Mathematics

Keywords

• Euler's elastica
• discrete curve
• discrete differential geometry

Details

• CRID: 1390853365588344704
• NII Article ID: 130008130446
• DOI: 10.14495/jsiaml.13.80
• ISSN: 18830617
• ISSN: 18830609
• Web Site: https://www.jstage.jst.go.jp/article/jsiaml/13/0/13_80/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed