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

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Abstract

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.

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Authors and Affiliations

  1. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, Russia

    S. Yu. Dobrokhotov, S. Ya. Sekerzh-Zen’kovich & A. A. Tolchennikov

  2. Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Region, Russia

    S. Yu. Dobrokhotov & A. A. Tolchennikov

Authors
  1. S. Yu. Dobrokhotov
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  2. S. Ya. Sekerzh-Zen’kovich
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  3. A. A. Tolchennikov
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Corresponding author

Correspondence to S. Yu. Dobrokhotov.

Additional information

The research was supported by the Russian Science Foundation, grant 16-11-10282

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Dobrokhotov, S.Y., Sekerzh-Zen’kovich, S.Y. & Tolchennikov, A.A. Exact and asymptotic solutions of the Cauchy–Poisson problem with localized initial conditions and a constant function of the bottom. Russ. J. Math. Phys. 24, 310–321 (2017). https://doi.org/10.1134/S1061920817030049

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  • DOI: https://doi.org/10.1134/S1061920817030049

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