On compactons induced by a non-convex convection

• The impact of a non-convex convection on formation of compactons is studied.
• Particulars of convection crucially affect the compacton dynamics.
• Both traveling and stationary compactons are possible.
• Some compactons may form only for a bounded range of velocities.
• Interaction of compactons may be close to elastic or undergo a fission process.

Using the model equation: ut±(u3-u2)x+(u3)xxx=0ut±(u3-u2)x+(u3)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.