{"title":"Linear stability of elastic 2-line solitons for the KP-II equation","authors":"Tetsu Mizumachi","doi":"10.1090/qam/1676","DOIUrl":null,"url":null,"abstract":"The KP-II equation was derived by Kadomtsev and Petviashvili to explain stability of line solitary waves of shallow water. Using the Darboux transformations, we study linear stability of \n\n \n 2\n 2\n \n\n-line solitons whose line solitons interact elastically each other. Time evolution of resonant continuous eigenfunctions is described by a damped wave equation in the transverse variable which is supposed to be a linear approximation of the local phase shifts of modulating line solitons.","PeriodicalId":20964,"journal":{"name":"Quarterly of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quarterly of Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/qam/1676","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The KP-II equation was derived by Kadomtsev and Petviashvili to explain stability of line solitary waves of shallow water. Using the Darboux transformations, we study linear stability of
2
2
-line solitons whose line solitons interact elastically each other. Time evolution of resonant continuous eigenfunctions is described by a damped wave equation in the transverse variable which is supposed to be a linear approximation of the local phase shifts of modulating line solitons.
期刊介绍：
The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume.
This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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