In the natural world, spectacular examples of singular wavefronts are seen in the form of the transbasin oceanic internal waves, whose characteristic feature is that their strongly nonlinear wavefronts reconnect when two collide transversely. The EPDiff equation has been proposed as a model for this phenomenon allowing for elastic collisions between singular wavefronts (solitons) whose momentum is distributed along curves moving in the plane. A series of 2d and 3d numerical simulations demonstrate the rich dynamics of solutions of the EPDiff equation in various scenarios.
|Author Institutional Affiliation
|LANL (Staley) and Imperial College (Holm)
|Patterns, wavefronts, epdiff