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Pré-Publication, Document De Travail Année : 2023

Asymptotic expansion of the solutions to a regularized Boussinesq system (theory and numeric)

Ahmad Safa
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Jean-Paul Chehab
Raafat Talhouk
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Résumé

We here consider the propagation of surface water waves described by the Boussinesq system. Following [9], we introduce a regularized Boussinesq system obtained by adding a non-local pseudo-differential operator define by g λ [ζ] = |k| λ ζk with λ ∈]0, 2]. In this paper, we display a twofold approach: First, we study theoretically the existence of an asymptotic expansion for the solution to the Cauchy problem associated to this regularized Boussinesq system with respect to the regularizing parameter ϵ. Then, we compute the function coefficients of the expansion (in ϵ) numerically and verify numerically the validity of this expansion up to order 2. We also check the numerical L 2 stability of the numerical algorithm.
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Dates et versions

hal-04177049 , version 1 (03-08-2023)

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  • HAL Id : hal-04177049 , version 1

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Ahmad Safa, Hervé Le Meur, Jean-Paul Chehab, Raafat Talhouk. Asymptotic expansion of the solutions to a regularized Boussinesq system (theory and numeric). 2023. ⟨hal-04177049⟩
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