KP-II方程弹性二线孤子的线性稳定性

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2023-07-19 DOI:10.1090/qam/1676

Tetsu Mizumachi

{"title":"KP-II方程弹性二线孤子的线性稳定性","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":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"pages\":null},\"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}","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

摘要

Kadomtsev和Petviashvili导出了KP-II方程来解释浅水线孤立波的稳定性。利用Darboux变换，我们研究了2个2-线孤子的线性稳定性。谐振连续本征函数的时间演化由横向变量中的阻尼波方程描述，该方程被认为是调制线孤子局部相移的线性近似。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Linear stability of elastic 2-line solitons for the KP-II equation

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

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.