Hamiltonian structure for null curve evolution

We construct a Hamiltonian structure for null curve motions in a three-dimensional Minkowski space. In order to define such a structure, a Lie algebra structure on variation vector fields along null curves is provided. Finally, we propose a new Hamiltonian evolution equation on null curves and the integrability of such equation is proved via a suitable connection with the Korteweg–de Vries equation. (paper)