{"title":"Convective Modulation Instability of the Radiation of the Periodic Component in the Case of Resonance of Long and Short Waves","authors":"","doi":"10.1134/s0081543823040107","DOIUrl":null,"url":null,"abstract":"<span> <h3>Abstract</h3> <p> The main result of the paper is a theorem stating that the modulation instability of a carrier periodic wave of small (but finite) amplitude propagating in an arbitrary dispersive medium may only be convective in a reference frame moving at a velocity that differs finitely from the group velocity of this wave. The application of this result to the radiation of a resonant wave by a soliton-like “core” is discussed. Such radiation occurs in media where classical solitary waves are replaced with generalized solitary waves as a result of linear resonance of long and short waves. Generalized solitary waves are traveling waves that form a homoclinic structure doubly asymptotic to a periodic wave. </p> </span>","PeriodicalId":54557,"journal":{"name":"Proceedings of the Steklov Institute of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Steklov Institute of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0081543823040107","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The main result of the paper is a theorem stating that the modulation instability of a carrier periodic wave of small (but finite) amplitude propagating in an arbitrary dispersive medium may only be convective in a reference frame moving at a velocity that differs finitely from the group velocity of this wave. The application of this result to the radiation of a resonant wave by a soliton-like “core” is discussed. Such radiation occurs in media where classical solitary waves are replaced with generalized solitary waves as a result of linear resonance of long and short waves. Generalized solitary waves are traveling waves that form a homoclinic structure doubly asymptotic to a periodic wave.
期刊介绍：
Proceedings of the Steklov Institute of Mathematics is a cover-to-cover translation of the Trudy Matematicheskogo Instituta imeni V.A. Steklova of the Russian Academy of Sciences. Each issue ordinarily contains either one book-length article or a collection of articles pertaining to the same topic.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
