The localized induction hierarchy and the Lund-Regge equation

Yasuhide Fukumoto, Mitsuharu Miyajima

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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 languageEnglish
Pages (from-to)8025-8034
Number of pages10
JournalJournal of Physics A: Mathematical and General
Issue number24
Publication statusPublished - Dec 21 1996

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy


Dive into the research topics of 'The localized induction hierarchy and the Lund-Regge equation'. Together they form a unique fingerprint.

Cite this