{"title":"非线性Klein-Gordon方程小能量呼吸子的渐近分析","authors":"Michał Kowalczyk, Yvan Martel","doi":"10.1007/s40818-026-00251-5","DOIUrl":null,"url":null,"abstract":"<div><p>For a general class of nonlinear Klein–Gordon equations, we prove that in the small energy limit, any sequence of breathers decomposes into a finite sum of decoupled, periodically modulated canonical solitons. Each of these solitons is asymptotically equal to an explicit sine-Gordon breather and the distance between them grows to infinity as the energy decreases to 0. Finally we prove that none of these breathers is centered in a bounded set provided that a certain non resonance condition holds.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"12 2","pages":""},"PeriodicalIF":3.0000,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymptotic Analysis of Small Energy Breathers for the Nonlinear Klein–Gordon Equation\",\"authors\":\"Michał Kowalczyk, Yvan Martel\",\"doi\":\"10.1007/s40818-026-00251-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For a general class of nonlinear Klein–Gordon equations, we prove that in the small energy limit, any sequence of breathers decomposes into a finite sum of decoupled, periodically modulated canonical solitons. Each of these solitons is asymptotically equal to an explicit sine-Gordon breather and the distance between them grows to infinity as the energy decreases to 0. Finally we prove that none of these breathers is centered in a bounded set provided that a certain non resonance condition holds.</p></div>\",\"PeriodicalId\":36382,\"journal\":{\"name\":\"Annals of Pde\",\"volume\":\"12 2\",\"pages\":\"\"},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2026-08-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pde\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40818-026-00251-5\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pde","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40818-026-00251-5","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Asymptotic Analysis of Small Energy Breathers for the Nonlinear Klein–Gordon Equation
For a general class of nonlinear Klein–Gordon equations, we prove that in the small energy limit, any sequence of breathers decomposes into a finite sum of decoupled, periodically modulated canonical solitons. Each of these solitons is asymptotically equal to an explicit sine-Gordon breather and the distance between them grows to infinity as the energy decreases to 0. Finally we prove that none of these breathers is centered in a bounded set provided that a certain non resonance condition holds.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
