### Abstract

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.

Original language | English |
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Article number | 235202 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Issue number | 23 |

DOIs | |

Publication status | Published - Jan 1 2014 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Journal of Physics A: Mathematical and Theoretical*, (23), [235202]. https://doi.org/10.1088/1751-8113/47/23/235202

**Discrete mKdV and discrete sine-Gordon flows on discrete space curves.** / Inoguchi, Jun Ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, no. 23, 235202. https://doi.org/10.1088/1751-8113/47/23/235202

}

TY - JOUR

T1 - Discrete mKdV and discrete sine-Gordon flows on discrete space curves

AU - Inoguchi, Jun Ichi

AU - Kajiwara, Kenji

AU - Matsuura, Nozomu

AU - Ohta, Yasuhiro

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84937029317&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937029317&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/47/23/235202

DO - 10.1088/1751-8113/47/23/235202

M3 - Article

AN - SCOPUS:84937029317

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 23

M1 - 235202

ER -