Estimate for the errors of asymptotic solutions of the Cauchy-Poisson problem

Asymptotic solutions of a Cauchy-Poisson problem, which are known in general form, are considered for Gaussian axially symmetric initial elevations of the free surface of fluid. Errors for the approximation of asymptotic solutions are presented in dependence on large dimensionless time. These errors were found in approximation of infinitely deep fluid and for the cases in which the ratio of the typical radius of the initial perturbation to the depth of the fluid belongs to the interval between a half and eight.