Hamiltonian flows on null curves

Details Hamiltonian flows on null curves Hamiltonian flows on null curves

2009-11-23

arxiv.org/abs/0911.4467v2

Nonlinearity23:2117-2129, 2010

Mathematics

Differential Geometry

14 pages, v2: final version; minor changes in the exposition

Scientific paper

10.1088/0951-7715/23/9/005

The local motion of a null curve in Minkowski 3-space induces an evolution equation for its Lorentz invariant curvature. Special motions are constructed whose induced evolution equations are the members of the KdV hierarchy. The null curves which move under the KdV flow without changing shape are proven to be the trajectories of a certain particle model on null curves described by a Lagrangian linear in the curvature. In addition, it is shown that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlev\'e equation.

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