{"title":"The inverse problem for periodic travelling waves of the linear 1D shallow-water equations","authors":"Robert Hakl , Pedro J. Torres","doi":"10.1016/j.physd.2024.134496","DOIUrl":null,"url":null,"abstract":"<div><div>For the linear 1D shallow-water system with a variable bottom profile, we study the inverse problem of the existence of a periodic bottom profile that allows a periodic travelling wave with prescribed amplitude <span><math><mrow><mi>q</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134496"},"PeriodicalIF":2.7000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278924004469","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
For the linear 1D shallow-water system with a variable bottom profile, we study the inverse problem of the existence of a periodic bottom profile that allows a periodic travelling wave with prescribed amplitude .
期刊介绍：
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.
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