INTERACTION OF NONLINEAR-WAVES AND THE FACTORIZATION METHOD

This note consists of two parts. In the first part we consider the interaction of incident and reflected waves in a non-linear rod. Exact formulae are obtained (and also estimates) for the extremal values of the stress in the region in which the incident and reflected ways interact. In the second part, which is a continuation of [1-6], a special asymptotic factorization of the non-linear wave equation is constructed, which enables an ordinary second-order differential equation to be derived, which describes the interaction of a short pulse and a simple wave moving in opposite directions. The amplitudes of the waves are assumed to be finite.