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Simple asymptotic solution of the Cauchy-Poisson problem for head waves. (English) Zbl 1179.35248

Summary: By using a modification of the method suggested in one of the works of V. A. Borovikov together with M. Ya. Kel’bert [Fluid Dyn. 19, 321–323 (1984); translation from Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 1984, No. 2, 173–174 (1984; Zbl 0551.76015)], 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.

MSC:

35Q35 PDEs in connection with fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics

Citations:

Zbl 0551.76015
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References:

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