Local geometric invariants of integrable evolution equations
Authors:
- 1 April 1994
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 35 (4) , 1732-1737
Abstract
The integrable hierarchy of commuting vector fields for the localized induction equation of 3D hydrodynamics, and its associated recursion operator, are used to generate families of integrable evolution equations which preserve local geometric invariants of the evolving curve or swept‐out surface.Keywords
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This publication has 26 references indexed in Scilit:
- Exact Solution to Localized-Induction-Approximation Equation Modeling Smoke Ring MotionPhysical Review Letters, 1986
- Lie groups, spin equations, and the geometrical interpretation of solitonsJournal of Mathematical Physics, 1980
- Rigid body motions, space curves, prolongation structures, fiber bundles, and solitonsJournal of Mathematical Physics, 1979
- Solitons and the Motion of Helical CurvesPhysical Review Letters, 1976
- Nonlinear Modulation of Gravity WavesJournal of the Physical Society of Japan, 1972
- Method for Solving the Korteweg-deVries EquationPhysical Review Letters, 1967
- Self-Induced Transparency by Pulsed Coherent LightPhysical Review Letters, 1967
- Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial StatesPhysical Review Letters, 1965
- A model unified field equationNuclear Physics, 1962
- Theorie der Versetzungen in eindimensionalen AtomreihenThe European Physical Journal A, 1953