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 Korteweg–de Vries (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, we show that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlevé equation.

Hamiltonian flows on null curves / Musso, Emilio; Nicolodi, L.. - In: NONLINEARITY. - ISSN 0951-7715. - STAMPA. - 23:(2010), pp. 2117-2129. [10.1088/0951-7715/23/9/005]

Hamiltonian flows on null curves

MUSSO, EMILIO;
2010

Abstract

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 Korteweg–de Vries (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, we show that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlevé equation.
2010
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2380873
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