Rotating Circular Peakons

Samuel Stechmann, New York University

Photo of Samuel Stechmann

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.

Abstract Author(s): Samuel Stechmann