The Korteweg–de Vries hierarchy as dynamics of closed curves in the plane
- 2 December 1991
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 67 (23) , 3203-3206
- https://doi.org/10.1103/physrevlett.67.3203
Abstract
The Korteweg–de Vries, modified Korteweg–de Vries, and Harry Dym hierarchies of integrable systems are shown to be equivalent to a hierarchy of chiral shape dynamics of closed curves in the plane. These purely local dynamics conserve an infinite number of global geometric properties of the curves, such as perimeter and enclosed area. Several techniques used to study these integrable systems are shown to have simple differential-geometric interpretations. Connections with incompressible, inviscid fluid flow in two dimensions are suggested.Keywords
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