Stationary and Self-Similar Waves in a Rod with Bimodular Nonlinearity, Dissipation, and Dispersion

Propagation of longitudinal elastic waves in a rod with bimodular nonlinearity, linear dissipation, and geometrical dispersion of phase velocity is analyzed. Analytical and numerical solutions are obtained for stationary and self-similar waveforms and pulsed perturbations that propagate in the rod without shape changes, and a corresponding graphical analysis is presented.