Solitary-Wave Interactions in Elastic Rods

The propagation of longitudinal deformation waves in an elastic rod is modelled by the nonlinear partial differential equation with p = 3 or 5. This equation is first derived under a range of possible constraints. We then show that this equation and even certain generalizations do not pass the Painlevé test, and hence are probably not completely integrable. Finally, we study the head-on collision of two equal solitary waves numerically and also asymptotically for small and large amplitude.