### Abstract

An evolution equation of a curve is constructed by summing up the infinite sequence of commuting vector fields of the integrable hierarchy for the localized induction equation (LIE). It is shown to be equivalent to the Lund-Regge equation. The intrinsic equations governing the curvature and torsion are deduced in the form of integrodifferential evolution equations. A class of exact solutions which correspond to the permanent forms of a curve evolving by a steady rigid motion are presented. The analysis of the solutions reveals that, given the shape, there are two speeds of motion, one of which has no counterpart in the case of the LIE.

Original language | English |
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Pages (from-to) | 8025-8034 |

Number of pages | 10 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 29 |

Issue number | 24 |

DOIs | |

Publication status | Published - Dec 21 1996 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Journal of Physics A: Mathematical and General*,

*29*(24), 8025-8034. https://doi.org/10.1088/0305-4470/29/24/025

**The localized induction hierarchy and the Lund-Regge equation.** / Fukumoto, Yasuhide; Miyajima, Mitsuharu.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 29, no. 24, pp. 8025-8034. https://doi.org/10.1088/0305-4470/29/24/025

}

TY - JOUR

T1 - The localized induction hierarchy and the Lund-Regge equation

AU - Fukumoto, Yasuhide

AU - Miyajima, Mitsuharu

PY - 1996/12/21

Y1 - 1996/12/21

N2 - An evolution equation of a curve is constructed by summing up the infinite sequence of commuting vector fields of the integrable hierarchy for the localized induction equation (LIE). It is shown to be equivalent to the Lund-Regge equation. The intrinsic equations governing the curvature and torsion are deduced in the form of integrodifferential evolution equations. A class of exact solutions which correspond to the permanent forms of a curve evolving by a steady rigid motion are presented. The analysis of the solutions reveals that, given the shape, there are two speeds of motion, one of which has no counterpart in the case of the LIE.

AB - An evolution equation of a curve is constructed by summing up the infinite sequence of commuting vector fields of the integrable hierarchy for the localized induction equation (LIE). It is shown to be equivalent to the Lund-Regge equation. The intrinsic equations governing the curvature and torsion are deduced in the form of integrodifferential evolution equations. A class of exact solutions which correspond to the permanent forms of a curve evolving by a steady rigid motion are presented. The analysis of the solutions reveals that, given the shape, there are two speeds of motion, one of which has no counterpart in the case of the LIE.

UR - http://www.scopus.com/inward/record.url?scp=0030597489&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030597489&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/29/24/025

DO - 10.1088/0305-4470/29/24/025

M3 - Article

VL - 29

SP - 8025

EP - 8034

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 24

ER -