Numerical study of the Amick–Schonbek system-Reference-Cited by-同舟云学术

Numerical study of the Amick–Schonbek system

Published:2024-04-04 Issue:1 Volume:153 Page:
ISSN:0022-2526
Container-title:Studies in Applied Mathematics
language:en
Short-container-title:Stud Appl Math

Author:

Klein Christian¹²^ORCID,Saut Jean‐Claude³

Affiliation:

1. Institut de Mathématiques de Bourgogne Université de Bourgogne Dijon Cedex France

2. Institut Universitaire de France

3. Laboratoire de Mathématiques Université Paris‐Saclay et CNRS Orsay France

Abstract

AbstractThe aim of this paper is to present a survey and a detailed numerical study on a remarkable Boussinesq system describing weakly nonlinear, long surface water waves. In the one‐dimensional case, this system can be viewed as a dispersive perturbation of the hyperbolic Saint‐Venant (shallow water) system. The asymptotic stability of the solitary waves is numerically established. Blow‐up of solutions for initial data not satisfying the noncavitation condition as well as the appearance of dispersive shock waves are studied.

Funder

Horizon 2020

Publisher

Wiley

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1111/sapm.12691

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