{"title":"Numerical study of the Amick–Schonbek system","authors":"Christian Klein, Jean-Claude Saut","doi":"10.1111/sapm.12691","DOIUrl":null,"url":null,"abstract":"<p>The 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.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 1","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/sapm.12691","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studies in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/sapm.12691","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
The 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.
期刊介绍：
Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.
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