Propagation of nonlinear waves in inhomogeneous hereditary media (Q1116808)

The propagation of a one-dimensional longitudinal wave with finite amplitude in inhomogeneous hereditary media with faded memory is considered. It is assumed that the elastic properties and the density of the medium vary smoothly along the direction of wave propagation. The wave motion is governed by the second-order nonlinear hyperbolic differential equation with coefficients depending on the space coordinate. The equation is solved by making use of the perturbation theory, the WKB method and the Laplace transform techniques. The solution obtained in the paper describes the initial stage of the distortion of the wave profile in its near-front region and satisfies the condition of the WKB solution, i.e. the variation of inhomogeneity is small on the characteristic length of the wave. The propagation of the sine-wave in an inhomogeneous standard viscoelastic medium is considered on the basis of this solution.