Simple asymptotic solution of the Cauchy-Poisson problem for head waves

Abstract

By using a modification of the method suggested in one of the works in 1984 by V. A. Borovikov together with M. Ya. Kel’bert, a simple asymptotic solution of the Cauchy-Poisson problem for the axially symmetric initial perturbation of power-law type is derived. It is shown that the solution thus derived describes the wave profiles of the head waves with high accuracy, in the cases of both very strong and weak dispersion.