Exact and asymptotic solutions of the Cauchy–Poisson problem with localized initial conditions and a constant function of the bottom
S. Yu. Dobrokhotov, S. Ya. Sekerzh–Zen’kovich, Антон Александрович Толченников · Russian Journal of Mathematical Physics · 2017
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.