Los Alamos National Laboratory is currently researching various properties of nonlinear shallow water wave equations. With the help of the Clinic’s Liaison, Dr. Darryl Holm, the team is analyzing the distinct behavior of the Camassa-Holm equation. This research investigation will include both a theoretical and a numerical analysis of soliton-like shallow water waves called peakons. For the numerical investigation, the team has created a numerical integrator for the third order, nonlinear Camassa-Holm equation. The theoretical results will be compared to numerical simulations that visualize various aspects of wave behavior in both the one and two dimensional cases.