On nonlinear plane vibration of a moving threadline (Q1102785)

We consider plane vibrations of a moving threadline described by the model equations obtained by \textit{W. F. Ames}, \textit{S. Y. Lee} and \textit{J. N. Zaiser} [Int. J. Non-linear Mech. 3, 449-469 (1968)]. We study the propagation of weak discontinuities and their interaction with shock waves. We show that the only possible shocks satisfying the Lax conditions and the evolutionary condition of \textit{L. Brun} [J. Mandel and L. Brun (eds.), Mechanical waves in solids (1975; Zbl 0374.73032)] are the characteristic shocks.