Spirals in Excitable Media

Spiral waves are remarkable structures observed in two-dimensional excitable media. They can be understood as deformations of half plane waves in the regime where the wave tip rotates on a circle which is much larger than the width of the one-dimensional pulse. We describe an asymptotic analysis of spirals and of their counterparts, retracting waves, from this viewpoint, in the free boundary limit where the propagating excited region is bounded by a sharp interface. Spiral drift in an imposed electric field is also described as an example of application of the analysis.