On the Uniqueness of a Self-similar Solution to the Riemann Problem for Longitudinal–Torsional Waves in Nonlinear Elastic Rods

Self-similar solutions to the Riemann problem for a hyperbolic system of two equations describing longitudinal–torsional waves in nonlinear elastic media with a negative nonlinearity parameter are studied. The solutions are constructed from a sequence of waves consisting of nonoverturning rarefaction waves and classical (Lax) discontinuities (shocks).