A. Karczewska, Maciej Szczeciński, P. Rozmej, Bartosz Boguniewicz
{"title":"Finite Element Method for Stochastic Extended KdV Equations","authors":"A. Karczewska, Maciej Szczeciński, P. Rozmej, Bartosz Boguniewicz","doi":"10.12921/cmst.2016.22.01.002","DOIUrl":null,"url":null,"abstract":"The finite element method is applied to obtain numerical solutions to the recently derived nonlinear equation for shallow water wave problem for several cases of bottom shapes. Results for time evolution of KdV solitons and cnoidal waves under stochastic forces are presented. Though small effects originating from second order dynamics may be obscured by stochastic forces, the main waves, both cnoidal and solitary ones, remain very robust against any distortions.","PeriodicalId":10561,"journal":{"name":"computational methods in science and technology","volume":"4 1","pages":"19-29"},"PeriodicalIF":0.0000,"publicationDate":"2016-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"computational methods in science and technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12921/cmst.2016.22.01.002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
The finite element method is applied to obtain numerical solutions to the recently derived nonlinear equation for shallow water wave problem for several cases of bottom shapes. Results for time evolution of KdV solitons and cnoidal waves under stochastic forces are presented. Though small effects originating from second order dynamics may be obscured by stochastic forces, the main waves, both cnoidal and solitary ones, remain very robust against any distortions.
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