On compactons induced by a non-convex convection

Using the model equation: u t ± ( u 3 - u 2 ) x + ( u 3 ) xxx = 0 we study the impact of a non-convex convection on formation of compactons. In the ( + ) version, both traveling and stationary compactons are observed, whereas in the ( - ) branch, compactons may form only for a bounded range of velocities. Depending on their relative speed, interaction of compactons may be close to being elastic or a fission process wherein the collision begets additional compactons.