Rotating Circular Peakons

Remarkable singular solutions called “peakons” exist for the PDE describing geodesic flow on the diffeomorphism group. Because the solution ansatz is a momentum map, the peakons evolve according to canonical Hamiltonian equations; thus the solution to the PDE has been reduced to the solution of a system of ODEs. I will show both analytical and numerical results for peakon solutions in the plane and on the sphere. Potential applications for these peakons include internal ocean waves and template matching.