Steady motion of hairpin-shaped vortex filaments in excitable systems.

We demonstrate the existence of steadily translating filaments in the Belousov-Zhabotinsky reaction. The filaments have self-reinforcing shapes tracing planar hairpins and constant velocities that are inversely proportional to their width. These features are well described by an analytical solution of the mean curvature flow problem. Using numerical simulations based on an excitable reaction-diffusion model, we also probe the solution's large basin of attraction and show that entangled hairpins reconnect during collisions.