The localized induction hierarchy and the Lund-Regge equation

Yasuhide Fukumoto, Mitsuharu Miyajima

Research output: Contribution to journalArticle

11 Citations (Scopus)

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 languageEnglish
Pages (from-to)8025-8034
Number of pages10
JournalJournal of Physics A: Mathematical and General
Volume29
Issue number24
DOIs
Publication statusPublished - Dec 21 1996

Fingerprint

Torsional stress
hierarchies
Proof by induction
induction
Evolution Equation
Intrinsic equation
Integrable Hierarchies
Curve
Motion
Integro-differential Equation
Torsion
Vector Field
Exact Solution
Curvature
curves
torsion
Hierarchy
curvature
Form
Class

All Science Journal Classification (ASJC) codes

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

Cite this

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

In: Journal of Physics A: Mathematical and General, Vol. 29, No. 24, 21.12.1996, p. 8025-8034.

Research output: Contribution to journalArticle

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