### Abstract

We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the WadatiKonnoIchikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sineGordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the EulerLagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations.

Original language | English |
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Article number | 395201 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 44 |

Issue number | 39 |

DOIs | |

Publication status | Published - 2011 Sep 30 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*44*(39), [395201]. https://doi.org/10.1088/1751-8113/44/39/395201

**Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves.** / Feng, Bao Feng; Inoguchi, Jun Ichi; Kajiwara, Kenji; Maruno, Kenichi; Ohta, Yasuhiro.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 44, no. 39, 395201. https://doi.org/10.1088/1751-8113/44/39/395201

}

TY - JOUR

T1 - Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves

AU - Feng, Bao Feng

AU - Inoguchi, Jun Ichi

AU - Kajiwara, Kenji

AU - Maruno, Kenichi

AU - Ohta, Yasuhiro

PY - 2011/9/30

Y1 - 2011/9/30

N2 - We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the WadatiKonnoIchikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sineGordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the EulerLagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations.

AB - We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the WadatiKonnoIchikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sineGordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the EulerLagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations.

UR - http://www.scopus.com/inward/record.url?scp=80052922138&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052922138&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/44/39/395201

DO - 10.1088/1751-8113/44/39/395201

M3 - Article

AN - SCOPUS:80052922138

VL - 44

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 39

M1 - 395201

ER -