Exact and asymptotic solutions of the Cauchy-Poisson problem with localized initial conditions and a constant function of the bottom

摘要

In the paper, the asymptotic solutions for a problem of Cauchy-Poisson type with localized initial conditions are constructed. The bottom of the basin under consideration which was constant before the perturbation, is instantly perturbed at the initial time moment by a spatially localized function. Simplifications of the corresponding formulas are presented inside and outside the vicinity of the leading front, as well as in the case of a special choice of the initial condition. It is shown that, in the vicinity of the leading front, the asymptotic solution coincides with the asymptotic solution of the linear Boussinesq equation.