长波和短波共振情况下周期成分辐射的对流调制不稳定性

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-09-01 DOI:10.1134/s0081543823040107

{"title":"长波和短波共振情况下周期成分辐射的对流调制不稳定性","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":"{\"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}","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

摘要

摘要本文的主要结果是一个定理，说明在任意色散介质中传播的小振幅（但有限）载波周期波的调制不稳定性，只能在以与该波的群速度相差有限的速度运动的参照系中对流。本文讨论了这一结果在类似于孤子 "核心 "的共振波辐射中的应用。由于长波和短波的线性共振，在经典孤波被广义孤波取代的介质中会出现这种辐射。广义孤子波是一种行波，形成与周期波双渐近的同次结构。

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

Convective Modulation Instability of the Radiation of the Periodic Component in the Case of Resonance of Long and Short Waves

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.

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

Proceedings of the Steklov Institute of Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

审稿时长

4-8 weeks

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.