Discrete mKdV and discrete sine-Gordon flows on discrete space curves

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

研究成果: Contribution to journalArticle査読

3 被引用数 (Scopus)

抄録

In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym-Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces.

本文言語英語
論文番号235202
ジャーナルJournal of Physics A: Mathematical and Theoretical
23
DOI
出版ステータス出版済み - 2014

All Science Journal Classification (ASJC) codes

  • 統計物理学および非線形物理学
  • 統計学および確率
  • モデリングとシミュレーション
  • 数理物理学
  • 物理学および天文学(全般)

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