The evolution laws of dilatational spherical and cylindrical weak nonlinear shock waves in elastic non-conductors (Q582961)

In the paper the evolution equations of dilatational spherical and cylindrical weakly nonlinear shock waves in elastic non-conductors is discussed. This includes some coupled equations giving the shock amplitude and the higher order discontinuities accompanying the shock process. The taken approach involves the use of the perturbation method with a perturbation parameter \(\epsilon\). The obtained results are compared to those known in nonlinear optics and this leads to a good agreement. We think the paper represents a fundamental contribution in the area of shock waves.