Numerical study of the Serre-Green-Naghdi equations in 2D

2023/06/16 by Sergey Gavrilyuk, C. Klein, Gavrilyuk, S. +1 · 1 citation
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2306.09731

openalex publication_date 2023/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

A detailed numerical study of solutions to the Serre-Green-Naghdi (SGN) equations in 2D with vanishing curl of the velocity field is presented. The transverse stability of line solitary waves, 1D solitary waves being exact solutions of the 2D equations independent of the second variable, is established numerically. The study of localized initial data as well as crossing 1D solitary waves does not give an indication of existence of stable structures in SGN solutions localized in two spatial dimensions. For the numerical experiments, an approach based on a Fourier spectral method with a Krylov subspace technique is applied.

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• Solitary waves of moderate amplitude and dispersive radiation in the Serre equations: the extended KdV-Whitham approximation

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