ON THE INTERACTION OF SOLITARY WAVES OF FLEXURE IN ELASTIC RODS

A numerical study is made to determine whether the partial differentia l equations governing planar, twist-free motions in a theory of the dy namics of elastic rods are completely integrable in the sense of solit on theory. The theory in which the equations arise is due to Kirchhoff and Clebsch and is complete to within an error of order two in an app ropriate dimensionless measure of thickness and strain. A recently dev eloped energy-preserving finite-difference scheme is employed to deter mine the consequences of the interaction of solitary traveling waves, which, in the present twist-free case, are loops traveling at constant speed. It is found that the change induced in such a loop-wave upon c ollision with another is more than a shift in phase.